The graph of a function f is is shown below. Sketch the graph of the derivative .

Question

The graph of a function f is is shown below. Sketch the graph of the derivative  .

Quizplus · Accepted Answer

The derivative of a function gives the slope of the tangent line at each point on the graph. Looking at the given graph, we can see that the function is increasing on the intervals (-∞,-2), (-1,1), and (3,∞) and decreasing on the interval (-2,-1) and (1,3). Therefore, the derivative will be positive on the intervals where the function is increasing and negative on the intervals where the function is decreasing. 
Option B is the only graph that satisfies this condition. The derivative is positive on the intervals (-∞,-2), (-1,1), and (3,∞) and negative on the intervals (-2,-1) and (1,3).

The Graph of a Function F Is Is Shown Below