Question

The total number of local maxima and local minima of the function

Answer 1

Find the total number of local maxima and local minima for the function

f(x)={(2+x)3(x)23if−3<x≤−1if−1<x<2f(x)={(2+x)3if−3<x≤−1(x)23if−1<x<2

My attempt : I differentiated the function for the two different intervals and obtained the following:

f′(x)={3⋅(2+x)223⋅(x)−13if−3<x≤−1if−1<x<2f′(x)={3⋅(2+x)2if−3<x≤−123⋅(x)−13if−1<x<2

How do I obtain the maxima and minima points from here.