Let $y = f ( x )$ be a differentiable function for which the graph of its derivative, ƒ ', is given below:
At what x-value(s), if any, does the graph of f have a local maximum?

A)x = 0 only
B)x = -3 only
C)x = 3 only
D)x = -3 and x = 3
E)None

Question

Let $y = f ( x )$ be a differentiable function for which the graph of its derivative, ƒ ', is given below:
At what x-value(s), if any, does the graph of f have a local maximum?

A)x = 0 only
B)x = -3 only
C)x = 3 only
D)x = -3 and x = 3
E)None

Quizplus · Accepted Answer

A local maximum occurs where the derivative changes from positive to negative. At x = 3, the derivative changes from positive to negative, indicating a local maximum.

Let y=f(x)y = f ( x )y=f(x) Be a Differentiable Function for Which the Graph of Its

Let $y = f ( x )$ Be a Differentiable Function for Which the Graph of Its