Question

The graph below shows graph of f (x), its derivative f '(x), and its second derivative f "(x). Which of the following is the correct statement?
A is f ', B is f, C is f ".
A is f ", B is f, C is f '.
A is f ', B is f ". C is f.
A is f, B is f ', C is f ".
I believe B is the original, C the first derivative, and A is the second derivative. Can someone please confirm this for me? Thank you!

Answer 1

Answer:

A is f ", B is f, C is f '.

Step-by-step explanation:

Your answer is correct.  B is the original function f.  It has a local maximum at x=0, and local minimums at approximately x=-3/2 and x=3/2.

C is the first derivative.  It crosses the x-axis at each place where B is a min or max.  C itself has a local maximum at approximately x=-3/4 and a local minimum at approximately x=3/4.

Finally, A is the second derivative.  It crosses the x-axis at each place where C is a min or max.