Jessie Green's Final Reflection

WOW..school is really over for the seniors. i don't really know how i expected to feel about this but now i just feel lost. no more pulling all-nighters for calculus tests, no more getting help from john or mrs. robinson, and no more fun together as the calculus class of 2010. i guess one of the things that stuck with me the most from this class was the strive to achieve a greater goal. derivatives, slopes, optimazation, and related rates are the things i remember most that i learned. not because i hated them but because these were the things i strived to learn first. through all the hard test and page long problems we learned how much we could better ourselves and take in mass amounts of information. as we all know one needs a teacher to learn how to do all of these problems and mrs. robinson was better than anyone we could ever imagine. she made learning everything fun and easier and because of her we can go to college and be truly prepared for what is waiting for us. to the calculus class of 2010 i just want to say thank you for such a wonderful experience and to mrs. robinson thank you for being willing to teach us:)!!!

the very first thing we learned this year was our derivatives:
d/dx c=0 (c is a #)
d/dx cu=cu' (c is #)
d/dx cx=c (c is a #)
d/dx u+v=u'+v'
d/dx uv=uv'+vu'
d/dx u/v=(vu'-uv')/v^2
d/dx sinx=cosx(x')
d/dx cosx=-sinx(x')
d/dx tanx=sec^2x(x')
d/dx secx=secxtanx(x')
d/dx cscx=-cscxtanx(x')
d/dx cotx=-csc^2x(x')
d/dx lnu= 1/u(u')
d/dx e^u=e^u(u')

other things that stressed us all out!!!:

linearization: The steps for working linearization problems are:
1. Identify the equation
2. Use the formula f(x)+f ' (x)dx
3. Determine your dx in the problem
4. Then determine your x in the problem
5. Plug in everything you get
6. Solve the equation

riemann sums!!:
The Riemanns Sums are:
LRAM-Left hand approximation=delta x[f(a)+f(a+delta x)+...f(b-delta x)]
RRAM-Right hand approximation=delta x[f(a+delta x)+...f(b)]
MRAM-Middle approximation=delta x[f(mid)+f(mid)+...]
Trapezoidal-delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
delta x=b-a/number of subintervals

Equation of a tangent line!!!!:
Take the derivative and plug in the x value.
If you are not given a y value, plug into the original equation to get the y value.
then plug those numbers into point slope form: y − y1 = m(x − x1)

Finding critical values!!!!:
To find critical values, first take the derivative of the function and set it equal to zero, solve for x. The answers you get for x are your critical values.

Absolute extrema!!!:
If you are given a point, plug those numbers into the original function to get another number. Alos, solve for critical values and plug those into the original function. Once you get your second numbers, you set each pair into new sets of points. The highest point is the absolute max and the smallest point is the absolute min.

volume by disks!!!:

the formula is pi times the integral of the [function given] squared times dx. so just solve it by taking the integral of it and then pluging in the numbers they give you. just like before you'll have two numbers so whatever the answer is for the top one will be first and then you subtract the answer you get for the bottom one. then graph

volume by washers!!!:

the formla is pie times the integral of the [top function] squared minus the [bottom function] squared times dx. so to do this, if you don't have the in between number you have to set the functions equal, but if you do, then it's worked the same way as above. square the formula's that were given and simplify. then take the integral of it and plug in the numbers they give you or you found by setting the formulas equal to each other and then solve like any other one by subracting them. then graph.

Limits!!!:

If the degree on top is smaller than the degree on the bottom, the limit is zero.
If the degree on top is bigger than the degree on the bottom, the limit is infinity.
If the degree on top is the same as the degree on the bottom, you divide the coefficients to get the limit.

First derivative test!!!:

You have to take the derivative of the function and set it equal to zero. Then solve for the critical values (x values). Set those values up into intervals between negative infinity and infinity. Plug in numbers between these intervals into the first derivative to see if there are max or mins or if the graph is increasing or decreasing.

Second derivative test!!!:

You take the derivative of the function twice and set it equal to zero. Solve for the x values and set them up into intervals between negative infinity and infinity. Plug in numbers between those intervals into the second derivative to see where the graph is concave up, concave down, or where there is a point of inflection.

Average rate of change !!!- f(b)-f(a)/(b-a).

2. Rate of change !!- this is simply a derivative! plug in an x value and get a slope out, your answer

3. Average value!! - this is 1/(b-a) times the integral from a to b of f(x). This is just an integral times by 1/(b-a).

4. Maximums, minimums, critical values, increasing, decreasing - all this is related to first derivative test. it's simple. you take the derivative, set equal to 0, solve for x. Set up some intervals using these numbers. Plug in numbers and test your intervals. pos to neg is a min. neg to pos is a max. pos = increasing, neg = decreasing. simple stuff. remember it.

5. Point of inflection, concave up, concave down - it's the second derivative test. set up intervals, if the intervals change signs, it is a point of inflection there. also, if its negative, that interval is concave down, positive is concave up.

6. Slope of a normal line - take derivative, plug in x. get a slope. however, make sure you use the negative reciprocal of the slope (normal means perpendicular to). use point-slope formula.

GOOD LUCK CLASS OF 2011!!!!!!!!!!!!! and may your senior year be filled with amazing times and fun:)

Love, Jessie Green:):):):)!!!!!!!!!!