The graph of the derivative of a continuous function f is shown.On what intervals is f decreasing? .
E) None of these

Question

The graph of the derivative  of a continuous function f is shown.On what intervals is f decreasing?  .
E) None of these

Quizplus · Accepted Answer

In order to determine when $f$ is decreasing, we need to look for intervals where the derivative $f'$ is negative (i.e. $f$ is decreasing when $f' < 0$).

Looking at the graph of $f'$, we see that it is negative on the interval $[-2,-1]$ and also on the interval $[1,2]$. Therefore, $f$ is decreasing on these intervals.

The answer choices are given in terms of their corresponding intervals for $f$. The only choice that includes both $[-2,-1]$ and $[1,2]$ is (C), so the answer is (C).

The Graph of the Derivative of a Continuous Function