The figure below shows the graph f ' the derivative of f, for -7<x<7. The graph of f ' has horizontal tangent lines at x=-3, x=2 and x=5 and a vertical tangent line at x=3.
A) Find all values of x, for -7<x<7, at which f attains a relative minimum. Justify your answer.
Upon analyzing the graph I came up with x=-3 and x=5 is the minimum because the part of the graph is concave up.
B) Find all values of x, for -7<x<7, at which f attains a relative maximum. Justify your answer.
At x=2 f retains a relative maximum because that part of the graph is concave down.
C) Find all values of x, for -7<x<7 at which f ''(x) < 0
***I just need to know if I got part A and B right, and if not what did I do wrong. And I need help with part C, could someone show me how to do it step by step? Thank you.