Local maximum/minimum of a cubic function
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...