Question

Suppose that f’’ is continuous everywhere. ( 4 points each)
a. If f’(-3) = 0 and f’’(-3) = 5, what can you say about f(x)?
b. If f’(5) = 0 and f’’(5) = -7, what can you say about f(x)?

Answer 1

\(\large\color{black}{ \displaystyle f'(-3)=0 }\)
\(\large\color{black}{ \displaystyle f''(-3)=5 }\)

this is what you have for part A?

Answer 2

You can say that the function is concave up at x=-3 (because the slopes are increasing which is given by the second derivative).

Answer 3

Also, you can tell there is a local minimum at x=-3.