The graph of a function f is is shown below. Sketch the graph of the derivative $f ^ { \prime } \text {. }$

Question

Quizplus · Accepted Answer

The derivative of the function is zero at the local maximum and minimum points of the function, and it is positive on the intervals where the function is increasing and negative on the intervals where the function is decreasing. Based on the graph, we can see that the derivative is zero at the local maximum point (the peak) and the local minimum point (the valley) of the function. The derivative is positive on the intervals (-∞,-2), (-1,1), and (2, ∞) where the function is increasing, and it is negative on the intervals (-2,-1) and (1,2) where the function is decreasing. Therefore, option B is the best choice for the graph of the derivative of the function.

The Graph of a Function F Is Is Shown Below f′. f ^ { \prime } \text {. }f′.

The Graph of a Function F Is Is Shown Below $f ^ { \prime } \text {. }$