the figure shows the graph of F', the derivative of a function f. the domain of the function f is the set of all X such that -3< or equal to x<or equal to 3

Question

a)for what values of x in the domain does f have a relative max and amin? justify
b) for what values of x is the graph of f concave up? justify your answer
c) use the information found in parts a and b and the fact that f(-3)=0 to sketch a possible graph of f

obiously you can not see the graph but can you give me instructions on how to do it?
thanks

Answer 1

In the domain -3 <= x <= 3

f has a max/min where f' = 0

f is concave up when f'' > 0. In other words, when f' is increasing.

f has inflection points where f'' = 0. In other words, where f' has a max/min.