I have a question that gives me the derivative graph (but not the function itself) of a cubic Function. The g '(x) is a parabola and is attached below:

Given the graph of g '(x), sketch g "(x) and a possible graph of g(x). Identify the following:

a) The interval where g(x) is increasing and decreasing

b) The local maximum and minimum points of g(x)

c) The intervals where g(x) is concave up and concave down

I have figured out the intervals where g(x) is increasing and decreasing as:

g '(x) > 0 when x < -5 and x > 1, therefore, g(x) is increasing

g '(x) < 0 when -5 < x < 1, therefore, g(x) is decreasing.

I have also attached what I have graphed as g(x) and g "(x).

Could anybody help me with finding the local maximum and minimum of g(x). I'm kind of stuck...