Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. $f ( x ) = - x ^ { 3 } + 3 x + 1$
A)
increasing on $( - \infty , - 1 )$
decreasing on $( - 1,1 )$
increasing on $( 1 , \infty )$
B)
decreasing on $( - \infty , 0 )$
increasing on $( 0 , \infty )$
C)
decreasing on $( - \infty , \infty )$
D)
increasing on $( - \infty , \infty )$
E)
decreasing on $( - \infty , - 1 )$
increasing on $( - 1,1 )$
decreasing on $( 1 , \infty )$

Question

Quizplus · Accepted Answer

By graphing the function on a graphing utility, we can visually determine the intervals over which the function is increasing, decreasing, or constant. The graph of the function has a local maximum at x = -1 and a local minimum at x = 1. Thus, the function is decreasing on the interval (-∞,-1), increasing on the interval (-1,1), and decreasing again on the interval (1,∞). Therefore, the correct choice is E.

Use a Graphing Utility to Graph the Function and Visually f(x)=−x3+3x+1f ( x ) = - x ^ { 3 } + 3 x + 1f(x)=−x3+3x+1

Use a Graphing Utility to Graph the Function and Visually $f ( x ) = - x ^ { 3 } + 3 x + 1$