Question

*photo attached* ap calc ab please help

i don’t really know how to picture what the graph of the derivative would look like

Answer 1

A) f'(3) < f'(0) < f'(-2)

Explanation:

You don't need to create a graph of the derivative. Remember that the derivative is the slope/rate of change of a function at a certain point!

At f(-2), you can see that the function is increasing around it, which suggests that f'(-2) is positive.

At f(0), you can see that the function doesn't increase nor decrease around it, which suggests that f'(0) is 0 (or no slope!).

At f(3), you can see that the function is decreasing around it, which suggests that f'(3) is negative.

This must mean that f'(3) < f'(0) < f'(-2)

I hope this clears things up, and please ask questions in the comments if you are still confused! I want to help you!