Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant.
$f ( x ) = 2 x ^ { 4 } - 4 x ^ { 2 }$
A) decreasing on $( 0,0 )$
increasing on $( 0 , \infty )$
B) increasing on $( - \infty , - 1 )$
decreasing on $( - 1,0 )$
increasing on $( 0,1 )$
decreasing on $( 1 , \infty )$
C) decreasing on $( - \infty , - 1 )$
increasing on $( - 1,1 )$
decreasing on $( 1 , \infty )$
D) increasing on $( - \infty , 0 )$
decreasing on $( 0 , \infty )$
E) decreasing on $( - \infty , - 1 )$
increasing on $( - 1,0 )$
decreasing on $( 0,1 )$
increasing on $( 1 , \infty )$

Question

Quizplus · Accepted Answer

The function $f(x) = 2x^4 - 4x^2$ is a quartic polynomial with two critical points at $x = -1$ and $x = 1$, where the derivative changes sign. Between these points, the function is increasing, and outside these points, it is decreasing, which matches option E.

Use a Graphing Utility to Graph the Function and Visually f(x)=2x4−4x2f ( x ) = 2 x ^ { 4 } - 4 x ^ { 2 }f(x)=2x4−4x2

Use a Graphing Utility to Graph the Function and Visually $f ( x ) = 2 x ^ { 4 } - 4 x ^ { 2 }$