Letter from a Birmingham Jail and the Birmingham Campaign

Paul Fischer

9/2014

Dr. Felicia Kornbluh

US History: the 60's

"I am in Birmingham because injustice is here."

Martin Luther King Jr. in Birmingham expanded the movement or Birmingham Campaign beyond the stuffy intellectual laws, decrying the "analysis" that had ineffectively left his people persecuted and poor, while standing up in a tangible and legitimate fashion for what he believed in. Nearly a generation after Gandhi, King shows that unguided protest invites brutality and effectively, if not for his own lifetime then for posterity, provides the case and leadership to fight back against the oppression, segregation, and disenfranchisement of African-Americans in the United States at the time.

At the time of the letter, the movement was the victim of a "broken promise" and Martin Luther King Jr. was facing a withdrawal and retreat from Birmingham. A key part, and he was told by supporters to not do this from lack of popular protest, was the involvement of children in his protest. By moving beyond the conventional means of protest including restaurant sit-ins and bus boycotts to involving the children immediately and directly affected by protest or inaction, Martin Luther King Jr. showed the full involvement and mobilization of these communities towards impacting the dire policies in place.

There are four basic steps to nonviolent campaign, which are outlined in the letter from jail. Then proof is provided that this has occurred in the campaign. The irony of Martin Luther King Jr. writing on whether “you are able to endure the ordeal of jail?” while in jail himself is not lost on the rhetorical power, repition and reinforcement make the letter itself, as a description of a campaign, an example of nonviolent maneuvers in a conflict. This is contracted in a sort of give and take contemporary discussion in the letter which takes multiple viewpoints into consideration while retaining the understanding that there is a common goal for those who will read his letter; it is for the doubting Thomases, the fellow supporters, and the soldiers of equality who marched with him themselves.

The intended audience is important as there is nothing in this letter that could infuriurate one of the oppositional persuasion, in fact it might even bring them around. That is a sign of nonviolent demonstration in itself. The mere point that in this campaign, outlined as a battle without violence, in the publicity of this letter the reverend invites his opponents and friends to the drawing board alike and still retains the moral rectitude and personal control to help them see the moral light as well as the opportunity to give his allies the tools to make progress.  The definition of just and unjust proves a pivotal point in this letter as it is explained that “an unjust law is a code that a numerical or power majority group compels a minority group to obey but does not make binding on itself” and in defining the parameters of action, there has been a philosophical or moral boundary that is crossed over which cannot be retreated.

Though there was ultimately a retreat from Birmingham, it was a retreat of victory. The letter was written, four young school girls had been killed in a church bombing and America began to see the power status quo as barbaric and brutal, reactionary in a silently murderous manner. By appealing beyond those at the planning table or drawing board, the most radical of his compatriots, and appealing to the country’s greater fear of communism, this letter may be written from a jail of defeat but it represents the call to action, like the Gettysburg Address for Abraham Lincoln in the Civil War that will give the Civil Rights movement the authority and power to dwarf and vigorously redefine the opposition as well as their own boundaries and goals.

In the end of the letter, a tribute is paid to those who are the most directly and abundantly targeted with this appeal. His fellow demonstrators, the “demo” teams that blew up American politics in the mid 1960’s, ones who may at the time have felt discouraged or afraid. They may have felt that the battle was uphill or steep, but as he quotes, “My feets is tired, but my soul is at rest” which is not a quote from Gollum of Lord of the Rings but an indication of the undying loyalty of those around him, and of the incipient and pervasive damage on the African-American population of under-education, health-care, and lower standards of living. It shows the willingness of his movement to carry out the battle until it is finished, and to do it on the terms which have been shown to work and are outlined by Martin Luther King Jr. in this letter.

Societal impact of currently under-regulated legal substances: Alcohol and Marijuana in comparison to lead

As seen in the Single Photon Emission Computed Tomography scan imaging, the cognitive damage from alcohol is legitimate; there is damage being done to the brain in significant and substantial amounts over any amount of use. In a heavy marijuana user, one region of the brain increased in function and activity, while the rest remained strong. It would appear that humans have become used to a level of alcohol (a naturally fermenting fruit rotting on the tree at late harvest will not have alcohol over .5%). For adults, while the damage is not permanent, it is significant, and by removing the toxins the brain has the capability of returning to normal. See the video below, posted before, to see an example of this.

What is the impact of this? It was in low and moderate marijuana users found to be nearly 5 points on average an increase in IQ (Fried et al.), there have been studies that suggest marijuana has a detrimental effect though this can be attributed to increased levels of toxoplasma gondii as marijuana is grown in greater amounts in home operations and has exposure to cat feces and has only been observed in states with illegal or decriminalized marijuana laws and recent exposure of leading anti-marijuana academics as corrupt and accepting corporate bribes without disclosing their anti-marijuana bias (Fang). Of low and moderate alcohol users: a "number of studies have noted a measurable diminution in neuropsychologic parameters in habitual consumers of moderate amounts of ethanol" (Eckardt). Taken into context, the estimated damage of lead poisoning (affecting the majority of Americans before the 90's or so, but today only affecting a minority) is 5-10 points  (Bellinger). Translated, as seen on the graph below, this means that the first toxin a population is exposed to will reduce the number of gifted (IQ of 125+) by 80% while when multiple of these are introduced, the bell curve flattens and the damage from 15 points for example will well within 85% (How Pollutants Affect Brain Development). Due to this nature of the bell curve and the improving environmental standards in the United States, there is now the capability to definitely recommend the regulation of alcoholic drinks and foods to under .5 percent.

It should be noted, however, that this graph is not perfectly accurate, and there is a skew on the graph towards a lower IQ where the population is more gradual, as seen demonstrated in actual IQ data below. This means that the effect that is being observed on the high end of the scale is "mirrored" on those with functional or mental retardation and with some substance there is no noticeable effect, and at some point there is an amount at which the number dramatically increase (closer to 20 or 30 points, perhaps associated with illegal narcotic or prescription drug use). An example of this can be seen by looking at the Chinese economy following the legalization of hard drugs in the 1800's which was associated with a loss of approximately 95% of the economy (Major Economies' Share of Global GDP, 0-2005) in just a few generations.

The economic impact of the loss of the gifted group is real, as IQ is directly correlated with achievement, productivity, and income. While the income difference between 90 and 110 IQ points is in the thousands or tens of thousands of dollars, from 110 to 125 or 130 can be over 500,000 dollars annually (seen below, extrapolating decile into percentile using an exponential scale). So it may only be two percent of the population that is substantially impacted by lead poisoning or unregulated alcohol and marijuana, but the impact to the economy is exponentially greater. This can be seen in the change in the workplace today, populations with clean environments, high-tech industry and low substance use rates have averages of 10 or 20, sometimes just 5 or 6 employees for each manager. Low tech industry in the 1960's involved hundreds of employees per manager or executive in companies and poorly qualified supervision. In countries and parts of the US with low environmental standards or high use rates this can continue to be seen, both legally and in illegal sweatshops.

Source: NLSY79, Bureau of Labor Statistics

By regulating the use of these substances to fall within safe levels, the cultural and societal benefits can be retained, while creating an artificial "Flynn" effect, where environmental factors such as health care, nutrition, or mating and marriage regulation and rules gives a boost to the population as seen below.

Addendum: Due to information on infection from toxoplasma gondii and resulting psychosis and schizophrenia that has only been compiled in a meta-analysis in 2014, the impact of marijuana on the IQ may be incorrect in places with legalized marijuana industries. It would appear that the most severe perceived negative effects of marijuana are in actuality the effect of a small parasite that is present in many cats, the fece of which will infect soil and crops in a home-grow operation for up to a year. The information provided here on the impact of illegal or decriminalized marijuana holds, however, as these laws encourage home grown operations meaning many users will contract the parasite as they will buy from a cat owner at some point. In addition the research was confounded using economic variables, and funding was sourced illegitimately to corporations in an investigation.

Bibliography:

Bellinger, David C., Karen M. Stiles, and Herbert L. Needleman. "Low-level lead exposure, intelligence and academic achievement: a long-term follow-up study." Pediatrics 90.6 (1992): 855-861.

Eckardt, Michael J., et al. "Effects of Moderate Alcohol Consumption on the Central Nervous System*." Alcoholism: Clinical and Experimental Research22.5 (1998): 998-1040.

Fried, Peter, et al. "Current and former marijuana use: preliminary findings of a longitudinal study of effects on IQ in young adults." Canadian Medical Association Journal 166.7 (2002): 887-891.

Fang, Lee. "Leading Anti-Marijuana Academics Are Paid By Painkiller Drug Companies | VICE News." VICE News RSS. VICE News, 7 Sept. 2014. Web. 20 Dec. 2014.

Fischer, P. A. (2014). Single Photon Emission Computed Tomography - Alcohol and Marijuana light use, case study.

Effect of under-regulated Marijuana or Alcohol on blood flow (circulation) of the brain

Effects of under-regulated or decriminalized regular or light marijuana and light alcohol use on the brain - Single Photon Emission Computed Tomography

These are the brains of various substance users, alcohol is seen to be incredibly damaging even in weekend only drinking, while marijuana use has an effect observed similar to caffeine. On the right are alcoholic and various other drug users. Using four times a week over the period of three years, this heavy drinker's brain is scalloped out, and damage to the blood circulation in the brain is apparent. In a normal person without any substance use and in continued sobriety, seen at the beginning, there is no damage to the circulation of the brain. Due to statistics suggesting infection from toxoplasmosis, the information provided here regarding marijuana, which is frequently homegrown may be incorrect, however it does show that marijuana use is equivocal to the effect of caffeine with responsible adult use. For those who experience more negative results with marijuana, potential toxoplasmosis gondii infection and hard substance use should be investigated (as both are linked and causal factors in schizophrenia and other disorder cases) and childhood history should be gathered and confirmed using a blood test for the stress hormone cortisol as well, as elevated cortisol levels have been identified as a primary causal factor in adult psychotic depression, and in childhood trauma victims, will be permanently higher (Belanoff). The scan remains an excellent example of light alcohol use as well as the impact of potential parasitic infection from using marijuana in a decriminalized or illegal setting. [Article from News Illustrated, 2013]

With the alcohol and other drug users, this looks like swiss or cottage cheese after decades or years of abuse. Interestingly and significantly, an example of a weekend only drinker is provided. The brain still looks completely decimated by the alcohol use, dismissing the concept that just sometimes using alcohol limits or reduces the damage done by the neuro-toxins present in alcoholic beverages. I wondered what might occur with light marijuana use (and much less alcohol use).
After about a year of sobriety (enough time for the circulation of the brain to return completely to normal), this experiment involved use of one half to one full ounce of marijuana and around 36 beers over a 6 month period and getting a single photon emission computed tomography scan which accurately shows brain function and substance use.

© MCT
Source: The Hanley Center, Amen Clinic, Siemens


First, it is necessary to look at a brain with bad habits and excessive caffeine use, this is a baseline:
                                                                     Daniel's Scan

Marijuana and alcohol use:

Over a six month period, occasional use of around 36 beers, seen following, moderate non-consecutive use and between one half and one full ounce of marijuana, medium quality consumed less than one half of a gram at a time. The damage to blood flow in the brain is clearly beginning in the same areas as that exhibited by an alcohol and marijuana user, though only a fraction of the levels as displayed through heavy use, and consistent with caffeine use. This indicates positively that light substance use has a legitimate and severe negative impact on multiple areas of cognitive and motor skill functioning as well as emotional processing, but is not nearly to the same level as some research has claimed. It must be noted, however, that in a legal setting the impact of pesticide and parasite free marijuana may be completely different from alcohol, and some studies have connected current light marijuana use, that is responsible adult use (5-10 grams per week in Fried et al.) with an increase in IQ (though alcohol remains negative regardless of legality). The scalloping seen on the top of the head is light, and most likely caused by alcohol consumption, along with reduced circulation to decision making and memory functions which are likely caused and exacerbated by marijuana consumption as well, though retrospective research using MRIs suggests that marijuana use may actually increase connectivity and alleviate these symptoms. There is currently no permanent structural damage, as expected as well. No significant history of physical brain trauma, ie. head injury or medical problems to rule out. Some prior use of hallucinogens including absinthe, but several years past and not apparent in this scan. It can also be mentioned before the experiment light alcohol use for 3.5 years and marijuana use for 5 years. The subject was 22 years old, and the brain seen is nearly complete in development, giving an accurate view of the substances involved.

Addendum: Retrospective research by several universities has found that the effects of marijuana on brain structure are such that responsible adult use increases functional connectivity in a dose dependent fashion, though this is only confirmed currently in IQ studies with responsible adult use of marijuana (Filbey). This may be due to different associations with light or heavy marijuana use and nonstandard quality, as noted in the study, "Long-term effects of marijuana use on the brain".

Second Addendum: Results may not be reproducible as lead contamination in marijuana has been confirmed in both Germany and the Northeast of the USA, both of which are regions in which the subject consumed marijuana under decriminalization procedures, a practice carried out by dealers of the historical artifacts to increase profits and potency. A similar research experiment in these regions recorded blood lead levels of around 3.5 micrograms per deciliter one month after cessation and urine THC levels were over 500 ng/mL (or over 10 times the level recorded in a chronic user 12 hours after use), suggesting the high core temperature of a lead-infused joint (1200 degrees centigrade vs. 700 in a cigarette or 500 in pipe tobacco) resulted in significantly more THC absorption than was previously believed. This is confirmed from studies on tobacco which show the absorbed nicotine from cigarettes is 5X greater than that of pipe tobacco, though research on THC absorption as a result of different incineration temperatures is not yet available. Finally, a case-study from Romania has recently shown that the short-term effects of THC are also positive, increasing alertness and even overwhelming the effect of "significant" alcohol intake, which decreased alertness until administration of THC brought the subjects to a level of cognitive functioning even above a control baseline level.

Imaging by Eclipse Nuclear Medicine
Facility: The Hanley Center

Affiliations: Undergraduate research completed while enrolled at the University of Vermont, no declared affiliations.


Bibliography:

Amen, Daniel G., and Martin Waugh. "High resolution brain SPECT imaging of marijuana smokers with AD/HD." Journal of psychoactive drugs 30.2 (1998): 209-214.

Belanoff, Joseph K., et al. "Cortisol activity and cognitive changes in psychotic major depression." (2014).

Callender, Thomas James, Lisa Morrow, and Kodanallur Subramanian. "Evaluation of chronic neurological sequelae after acute pesticide exposure using SPECT brain scans." Journal of Toxicology and Environmental Health, Part A Current Issues 41.3 (1994): 275-284.

Filbey, Francesca M., et al. "Long-term effects of marijuana use on the brain." Proceedings of the National Academy of Sciences 111.47 (2014): 16913-16918.

Fried, Peter et al. “Current and Former Marijuana Use: Preliminary Findings of a Longitudinal Study of Effects on IQ in Young Adults.” CMAJ: Canadian Medical Association Journal 166.7 (2002): 887–891.

Mariani, Giuliano, et al. "A review on the clinical uses of SPECT/CT." European journal of nuclear medicine and molecular imaging 37.10 (2010): 1959-1985.

Torrey, E. Fuller, John J. Bartko, and Robert H. Yolken. "Toxoplasma gondii and other risk factors for schizophrenia: an update." Schizophrenia bulletin 38.3 (2012): 642-647.

NASA Gamma Ray Burst Notes 11.22.2013

Gamma Ray burst

first in six

observed from underground observatory

DRV130427A

Dying star in distant galaxy

one o the brightest we have ever seen

never before seen details challenge our theoretical understanding of how gamma ray bursts work

Charles Dalmer

Astrophysicist in DC, Naval research Laboratory

High energy radiation outbursts

Tom Vestrand

LANL

watches night sky for extra terrestrial objects and things that go bump in the night

Rob Triess

University of Alabama astrophysics

GBM triggered on event on april 27

Interesting behaviour on the first burst of the pulse

Jean-pieroo natafili

Italian Astrophysicist

Gamma ray bursts on laser

new development of telescopes

Sylvia Zoo

Astrophysicist, Maryland

Grad Student

High energy emission from Gamma Ray Bursts

Space craft was able to look at the burst as well as the lab

3 Nasa spacecraft observed gamma ray burst

A Gamma Ray Burst: trans insomething burst of gamma ray radiation from some object in space. after decades of research we find that those gamma rays come from birth of black hole in most cases, this was just an imitation, but only through the development of neew ways of looking to reorient space craft very quickly to get a look at these bursts…

Potential damage of a GRB?

Depends on distance, and if it was pointed at earth (unlikely). atmosphere will generally absorb gamma rays, billions of lightyears away normally. if there was a burst in your galaxy, strong possibility of electronic pulses and ionizing radiation, after time the ozone layer would be destroyed, allowing more radiation and nitrogens would be released, leading to a nuclear winter

why is it important to study GRB?

good question but rhetorical. What was the purpose of uranium study in the early 1900's what was the significance of studying sun burning in the 60's? We do not think this will change the world, but this is an explosion and explosion studies have intrinsic value in field of particle beams and uses to give us greater appreciation of all that occurs in nature.

Tremendous amount of energy in GRB, where does it come from?

Ill pipe up and say in large part we do not really know. The bright part of 13027A is that we can study the bright parts in detail, made possible by Dr. Goerner and ensure that everything goes according to the radiation. We know that energy is directed very efficiently, and seems to convert energy into radiation naturally. Our attempts to do so have fallen flat.

What do scientist learn from studying this?

We were able to identify the first and by doing this we could find a good position and recht we immediately too that these objects were intergalactic and we understood these were very powerful objects, which is useful. There is the object in the radio, 98 percent of the weere Dja gamma ray bursts, it is the most effective way the band to tell theposition and the other band that peopled can follow with instrumentation.

People relate this amount of energy to an atomic bomb. How many atomic bombs would this be equivalent to?

wikipedia says that the most powerful hydrogen bombs released about 15 megatons of TNT equivalent energy. You would need 10^30 of these bombs to have one of these bursts. 

Are these directed in one direction or omnidirectional?

Highly directional. In this particular case, the relatively narrow beam would have to be pointed directly at us.

OK How did one of these spacecraft target this area dn saw the burst before during and after?

The difference between monocular and technicolor. Multiple observations give you so much more information. The earth was not blocked on 1427A so there was allowed onboard triggering and response to move the spacecraft to view the burst. No imaging to know the counterpart without detailed X-rays and other information

More than the electromagnetic spectrum, we are in the EM channels but as time goes on they behave in different manners. Intimate clothing makes another separate high energy radiation situation. Multiple complicated wavelengths

Can one of these occur in our galaxy?

one ever 100 million or 500 million years. these numbers are not certain, but it is something we can expect.

How frequent are these observed?

We have a good idea from orbiting observatory which except for earth blockage we saw the entire sky with gamma rays neural the entire universe with bursts. One per day per universe. So the universe provides that, but we do not know where or when.

How can these bursts affect us if they happen here?

They can if they are in the Milky Way, and one is not really expected here. Might change the atmosphere, perhaps if close by some minor changes could be expected.

Any plans for gamma ray burst science that is coming up?

We are in kind of a climate where we do not anticipate high energy astrophysics new projects. we have two good observatories in orbit andwe have a good life expectancy. The Chinese are planning a follow up in Guam.

If there is an agreement this would happen 1015 2016 probably

Is there a program in place to find or predict the next event?

Lots of attempts ot find a demonstration, we have been able to identify certain stars that are likely to have such an event in their area. Typically at such large distances we cannot see individual stars. Liklihood of such a program being approved is not very likely.

Antimatter?

Model of matter-anti matter shows there is a sizzling layer between the two so there is not lots of emissions except for comets which do not work, i was playing with that.

Locations?

we have plotted them out and they are isotropic. so that is the challenge of building observatories that can observe these at anytime anywhere. no sweet spot to look at.

When one of these assets is in the GRB, what is implicated?

notices are sent out to subscribing astronomers with the BAT instrument and each is hooked into the service and sends information out to interested astronomers. Remote telescopes pick up these messages from the internet real time and reposition to view what is occurring. One of the interesting observational challenges is looking at the gamma ray burst before the explosion occurred. This happened before the event development through the act.

How often can we expect to see a GRB of this size?

Typical of gamma, what is unusual is how near by this  burst was. Every 60 years or so we can infer this sort of event happens once or twice very unique every century.

Whatis interesting here/?

persistent afterglow (optical) we knew about this but this one is beautifully interesting because there is such persistence of high energy gamma rays. This persistent gamma ray is caused by some shock etc…

how does this GRB compare to photo extinction event?

first one has to convince people studying that a major extinction event was causedby GRB, personally thinks it is due to volcanic activity. within the milky way it would have to oerate.

one thing that is sot interesting is that the cataclysmic event happened over an extended period. but the gamma ray burst would be  a one - two punch. so the cosmic rays can cause global cooling. There are some behavioural extinction that occurs within those patterns. The patterns in the galaxy are so rare and unlikely, we like to think this is not the case despite tantalizing suggestion.

how big can a gamma ray burst get? upper levels?

The seem to originate in massive stars. All the energy that is equivalent to the rest mass of the sun is equivalent to the mass of the sun. these are isotropic events that are equivalent to outflows and jets, the upper limit is determined by the size of the star that is the preginature of the burst.

How does the GRB actually start?

the most energetic GRB: not proven that black holes are the power, could also be certain stars, for example evidence in plateaus from swift telescope. In many occasions this is pullover. can be monitored in terms of absolute energy. Directed into a very small jet we get very small bursts. We have to figure out what we see versus what really is. This is a difficult or tricky situation to evaluate.

How do they Start!

There is a massive star with fuel and that fuel is spent, put under neutrons degeneracy pressure, yields a black hole, natural situation. 

Is the Gamma Ray Radiation so to speak a beam like a laser?

No and no.

Is there enough energy that it fuses the heaviest elements?

Conference in Kudo where modelling of fusing into higher atomic mass elements was assimilated and it seems to a pretty good approximation gives the highest level elements, so the possibility is yes we can produce some fraction of the heavy metals involved. Excellent question because it ties to how these are related. there would not be a supernova formation event. people look at gamma ray events where black hole is forming massive satr.

Why is there a difference?

The optical light is generated often by lower energy particles and maybe accelerated in different ways. From optical illusion, we think they are generated by exactly the same process. With this other type of optical illusion which we see it is kind of the glowing embers of the explosion, if you will. But not at these lower energy gamma ray emissions, we will often see after these GRE.

Terrestrial GRB?

terrestrial gamma ray flashes are by fermee no way to object the fields of electrons over electric storms. and we see energies high enough to produce pares of electrons and positrons. also quite interesting but a completely different phenomenon

What do X-rays bring to the table in GRB study?

We see some evolution occurring. It sees then that whitefish the spectrum doesn ot change over housr minutes and days. it is some level of information from before. even there we thought the spectrum was exactly the same up to 73. but this was also interpretation as well compared to modern interpretation.

anything else?

it was interesting in the lab because it gave us pop to study something far away and normally something this close is weak, but this was more of an ordinary monster, but close to earth. previously we had a model that explains the HEE very well. We did not see things before when the bursts were very close to us. For these events we required that we think back or tweak our models or something. Also because it was so close we had to observe for 20 hours, something with HEGR.

We saw this on 4/27 but how long did it take for that energy to get to us? when was it born?

black hole was born about 3.75 billion years ago, so this was a young burst all the same, because many we see are 5 or 10 billion years old. Because it is young the signal is very strong. when the earth was then, it looked very different and the whole universe looked different.

The important question is how to measure distance and that is astronomy?

Chuck was lost.

Could the GRB signal an extinction event on mars? such as disappearance of an atmosphere?

No, it is very different, off the road ap, very unlikely. 

Can we assume the burst occurs as a creation event of every black hole?

it is very likely that these happen when a very massive star, the core of one into another. highly magnetized neutron star. so not entirely accurate to say each of these has a black hole, and also not true that all black holes come from this.

What is the effect of gravity on this explosion?

detailed modelling of the collapse of a massive star into nothing, yields a lot of damage giving characteristic signature on gamma ray waves. should be simultaneous, and gravity wave radiations.

Vapor with the optical data, if this interpretation is correct we look at less than 3 million degrees. but his is not cut, there is a discussion about it. a few degrees.

Has this burst actually changed any of our understanding about how stars evolve?

no, because apart from the energy emission it is very similar to the other GRB, what is actually this burst, we can see the Supernova, usually associated to very long bursts, much weaker. This is not very far away, and we can see the entirety of the burst, usually one or two up to 6 or 7 or 9 we have seen so far, something supernova.

Notes for Calculus 1 - CYR

Chart is key to doing this type of problem

f'(x)=4x^3-48x=0

4x(x^2-12)=0

x=0 or x^2-12=0

=>x^2=12

x=2+-(v--3)

f''(x)=12x^2-48=0

12(x^2-4)=0

12(x+2)(x-2)=0

x=+-2

-4 -3 -1 1 3     4

    (-@@,-2V--3)|(-2V--3,-2)|(-2,0)|(0,2)|(2,2V--3)|(2V--3,@@)

f'(x)+-     |(-) (+)     (+)     (-)       (-)     (+)

f''(x)+-     |   (+)                       (+)     (-)       (-)       (+)            (+)

inc/dec     | dec inc     inc     inc    dec       inc

concave up/down|up up     down down up     up

sketch     |          U intersect(grk) U

noticing mirror like combinations of positive to negative values, whengl

f'(x)=4x^3-48x

=4x(x^2-12)

f'(-4)=4(-4)((-4)^2-12) will be negative

f'(-3)=4(-3)((-3)^2-12)positive

f'(-1)=4(-1)((-1)^2-12)positive

extrapolated application of number to variables

rel max @ (0,f(0))

rel. min.@ (2V--3, f(2V--3)) and -2V--3, f(-2V--3)) (2root3, -66) and (-2root3, -66)

f(x)=x^4-24x^2+80

f(0)=80

f(2V--3)=16*9-24(4*3)+80

146-288+80=0

=-146+80= -66

^^same as f(-2V--3)

Exam Prep

Relative Extreme

very similar to what we get on the test, parts a  thru e

just fill in all the blanks

not too hard, just to remember what is going on

any specific questions or walkthrough?

some derivatives?

probably one that involves more than one rule

List out all the rules-2columns

1) first side:

Derivatives we know

f(x)=x^n

=polynomial

e^x or a^x

ln^x

sinx cosx

2) rules to use we can "break up functions"

product rule u(x)-v(x)

quotient rule: p(x)/q(x)

chain rule: u(v(x))

ex) f(x) = sin^2(x+1/x)

=(sin(x+1)/(x))^2

CHAIN RULE

u(x)=x^2

u'(x)=2x

v(x)=sin((x+1)/x)

chain rule again

g(x)=sinx

g'(x)=cosx

h(x)=(x+1)/x

h(x)=(x/x)+1/x)

h'(x)=x^-2

v'(x)=g'(h(x))*h'(x)

=cos((x+1)/x)(-x^-2)

=-cos((x+1)/x)/x^2

f'(x)=u'(v(x))*v'(x)

2(sin((x+1)/x)(-cos((x+1)/x)^2)

ex) f(x)=(x^2-2)/e^x^2

Quotient rule: 

p(x)=x^2-2

p'(x)=2x

q(x)=e^x^2

CHAIN RULE: q=u(v(x))

u(x)=e^x

u'(x)=e^x)

v(x)=x^2

v'(x)=2x

q'(x)=e^x*(2x)

f'=(e^x^2*2x-(x^2-2)(2xe^x^2))/(e^x^2)^2

=(2xe^x^2)-(2x^3e^x^2)+(4xe^x^2)/(e^2x^2)

=(xe^x^2)(6-2x^2)/(e^x^2)^2

=x(6-2x^2)/(e^x^2)

f(x)=3xe^x+2

find where ifs inc/dec,

concave up/down

PRODUCT RULE

u(x)=3x 

u'(x)=3

v(x)=e^x

v'(x)=e^x

f'(x)=3e^x+3xe^x

3e^x+3xe^x=0<- to find CNS

3e^x(1+x)=0 e^ ANYTHING IS NEVER ZERO

1+x=0

x=-1 CN

f'(-2)=3e^-2(1-2)

f'(0)=3e^0(1-0) --> Positive!

f is increasing on interval (-1,@@)

and decreasing on (-@@,-1)

would increase product rule but we are smart and we realize hey, this is the derivative of 3xe^x

f''(x)=3e^x+(3e^x+3xe^x)

6e^x+3xe^x

3e^x(2+x)=0

x=-2

f''(-3)=3e^-3(2-3) gives NEGATIVE

f''(0)=3e^0(2-0)>0

f is concave up on (-2,@@)

down on (-@@,-2)

only way we know when it goes up to down is at inflection points

149 at drug test lab ate one pack of old (hard) swedish fish

ray expected to call in 45 minutes or an hour

ray never calls, tells me to fuck off when I call him> NO DRUG TEST TAKEN

Must find rent.

Lou Reed

Heute ich bin seemlich traurig in jede lebensweg. Untergestern Lou Reed, famous rocker, gestorben ist. Ich habe zwei mal musik filmen von youtube uber ihnen Band, Velvet Underground, gemacht. Ich mochte etwas mehr zu machen, ich fuhle das fur eine musiscian, artisten, und figure influential, wir (den Weld) zu kleine macht sind. Aber ins gleich sagen, fuhle ich die fur dem passierten wielleicht darr keine tribute genug wurde. Mann kann nur seinen musik horen und denken von wohin er kammt, und was dafur er arbeitet. Arbeitet die falsche wurde ist, er spielt und er beweigung hatte, dass fur den decadense und von dem arme. Seine influence positif und negatif gleich ist, aber ich seine hertz von Gold macht wurden glauben wollte.

Heute bin ich (in jeder Hinsicht?) ziemlich traurig. Vorgestern ist Lou Reed, ein berühmter Rockstar gestorben. Ich habe zwei Youtubevideos über seine Band Velvet Underground gemacht aber ich habe das Gefühl, dass das nicht genug ist. Ich würde gerne mehr machen, aber vielleicht ist das Gefühl normal, weil man einem so großen und einflussreichen Künstler nicht genug Tribut zollen kann. Vielleicht ist es genug seine Musik zu hören und daran zu denken, woher er kam und wofür er gearbeitet hat. Arbeiten ist hier wohl das falsche Wort. Ihm lagen Arm und Reich gleichermaßen am Herzen und auch wenn sein Einfluss sowohl positiv als auch negativ war, möchte ich doch glauben, dass er ein Herz aus Gold hatte.

-Corrected by Anna-Lisa of Augberg