Post #4

This week was a really short week in calculus. We were off Monday, Tuesday and Wednesday Mrs. Robinson wasn’t at school, and Thursday I wasn’t there so that only leaves Friday. Since I missed Thursday, those notes are what I am most confused about. I copied the notes, but I don’t understand how to find differentiability or what we do with it when we find it if we do anything at all. Friday we learned the second derivative test and I think I understood it pretty well. It is the same steps as the first derivative test, but instead of using the first derivative, you have to find the second derivative.

The steps include:
1. Take the first derivative
2. Take the second derivative
3. Set it equal to 0 and solve for x
4. Set up intervals
6. Plug in second derivative
7. Find points of inflection

Ex: f(x) = 6/ x^2=3

First derivative: (x^2+3) (0) – [(2x) (6)]/(x^2+3)^2 which equals -12x/(x^2+3)^2

Second derivative: (x^2+3) ^2 (-12) – [(-12x) (2 (x^2+3)) (2x)]/(x^2+3) ^4When simplified it comes out to 36 (x+1) (x-1)/(x^2+3) ^3

Set the top equal to zero: 36(x+1) (x-1) =0 and solve for x which equals x=1 and x= -1

Set up intervals: (-infinity, -1) (-1, 1) (1, infinity)

Pick a number between and plug into second derivative: f (-2) = positive = concave up, f (0) = negative = concave down, f (2) = positive = concave up.

Points of inflection is where the graph changes concavity which is at x=-1 and x=1.

The last step is to justify your answer.

It would also help if someone can tell me what is on the quiz tomorrow.