Sketch the graph of derivative f ′(x), clearly showing where f ′(x) is positive and negative, and giving intervals where f ′(x) is increasing or decreasing.

Question

Answer 1

The red graph is the f(x), the one you have given and the blue graph is the f ' (x)

x < -3, f ' (x) is decreasing

x = -3, f ' (-3) = 0 (critical point)

-3 < x < 0, f ' (x) is increasing

x = 0, f ' (0) is undefined (critical point)

x > 0, f ' (x) = - 4