The graph of the derivative $f ^ { \prime } ( x )$ of a continuous function $\mathrm { f }$ is shown. On what intervals is $f$ decreasing?

A) $( 1,3 ) \cup ( 4,6 )$
B) $( - 1,1 )$
C) $( 8,9 )$
D) $( 2,6 )$
E) None of these

Question

The graph of the derivative $f ^ { \prime } ( x )$ of a continuous function $\mathrm { f }$ is shown. On what intervals is $f$ decreasing?

A) $( 1,3 ) \cup ( 4,6 )$ 
B) $( - 1,1 )$ 
C) $( 8,9 )$ 
D) $( 2,6 )$ 
E) None of these

Quizplus · Accepted Answer

The intervals where the derivative is negative correspond to intervals where the function is decreasing. Looking at the graph, we see that the derivative is negative on $(1,3)$ and $(4,6)$. Thus, the function is decreasing on those intervals.

The Graph of the Derivative f′(x)f ^ { \prime } ( x )f′(x)

The Graph of the Derivative $f ^ { \prime } ( x )$