Question

I have a picture below, I was wondering how I would find the relative max,min from looking at the graph of g'.
On (-5,8) find the x values of all relative max, and relative min of g(x).

Answer 1

Think about what you do with the derivative test for finding extrema.

Extrema occur at points for which the derivative is zero. So if the derivative is zero at \(x=c\), then \(x=c\) is a minimum if to the left of \(c\) the derivative is negative, and a maximum if to the right the derivative is positive.

Otherwise, \(x=c\) is a maximum if to the left, the derivative is positive and to the right, it's negative.