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 minimum?

A)x = 0
B)x = -2
C)x = -2, x = 1, and x = 0
D)x = 1
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 minimum?

A)x = 0
B)x = -2
C)x = -2, x = 1, and x = 0
D)x = 1
E)None

Quizplus · Accepted Answer

A local minimum of the function $f(x)$ occurs where its derivative $f'(x)$ changes from negative to positive. In the given derivative graph, this transition only happens at $x = 1$.

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