Question

Find the interval in which the following function is increasing or decreasing.
$f\left(x\right)=2x^3-24x+7$

Answer 1

Given,

$f\left(x\right)=2x^3-24x+7$

$f^{\prime }\left(x\right)=6x^2-24$

put $f^{\prime }\left(x\right)=0$, for critical points

i.e., $6x^2-24=0$

$x^2-4=0$

$x=\pm 2$

Clearly, $f^{\prime }\left(x\right)>0$ if $x>2$ & $x<-2$

$f^{\prime }\left(x\right)<0$ if $-2<x<2$

Thus, $f\left(x\right)$ is increasing in $(-\infty ,-2)\cup (2,\infty )$, decreasing in $(-2,2)$.