17th post

This week in calculus we took two practice AP exams. One was calculator allowed and the other one was not. I found them to be hard but i didn't do to bad on them lol. Anyways, i'll start off by telling some of the things i know pretty well:

Average Value:

This is something i didn't always understand but today i learned how to do it and it seems pretty easy to me now. You start by understand you will have a number in front of the integral and you find it by 1/b-a... then you have to integrate the function and plug in the numbers. Once you have done that you solve.

Another thing i understand well is Rolle's Theorum: If the function is continuous and differentiable when you plug in the two points they give you.. then Rolle's Theorum can be used. After that, you take the derivative of the function and set it equal to zero and solve for x. Your x value will be your answer.

For mean value theorum, you also have to figure out whether the function is continuous and differentiable by plugging in the points given in the original function. This time, instead of setting the derivative equal to zero, you set it equal to the slope of b and a. To find the slope, you plug into f(b)-f(a)/b-a. Then you set the derivative equal to that number and solve for x.

Another thing is finding critical values. To find critical values, you take the derivative of the function and set it equal to zero and solve for x. What ever number or numbers you get for x is your critical values. Absolute extrema is pretty simple as well. If they give you a point in the problem, then you plug those numbers into the original function to get another number. You also solve for your critical values and plug those into the original function as well. Once you get your second numbers, you set each pair into new sets of points. Your highest point will be your absolute max and you smallest point will be your absolute min.

For some things i do not understand:
I am still having trouble with the trapezoidal rule. I am also having problems with trig inverse functions and solving for x with them and setting them up into intervals. If anyone can help me i would appreciate it. Thanks :)