Post #5

This week we basically reviewed for the test on Monday. After getting together with a couple of people for a study group, I understand some concepts that I didn't know before. So overall, I think I'm somewhat prepared for the test. I can do the First and Second Derivative Tests with my eyes closed. And then we learned how to find absolute max and mins which is even easier than the Tests. For example:

Find the absolute extrema(max and mins) of f(x) 1/(x^2 + 1) on [-1, 1].

After taking the derivative by the quotient rule you get:

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

Set the top equal to zero and it gives you x = 0. Then set up your intervals with you given interval.

(-1, 0) U (0, 1)

Plug in your critical values and your intervals into the original function to get your y values. So you will have (-1, 1/2), (0, 1), (1, 1/2).

Since 0 gives you the biggest value, there is an absolute max at x=0. And from what I understand, -1 and 1 are not mins because there are two of the same values. Someone might want to clarify that for me.

Justification: By using the 1st Derivative Test, I set the derivative equal to zero and solved for x. I then plugged my critical values and endpoints into the original function and found an absolute max at x=0.

Couls someone please explain the graphs to me? Like when you're given a graph of the second der. and asked to find the graph of the original. I know what it looks like and can eliminate a couple of choices, but I usually cannot decide between the two or three left. That whole study packet on graphs kind of confused me, and I could really use some help. Also, for some reason I have difficulties graphing a function after finding the extrema and such, but that could just be because I fail at graphs. Thanks :)