Question

Find the interval in which the following function is increasing or decreasing.
$f\left(x\right)=2x^3+9x^2+12x-1$

Answer 1

Given,

$f\left(x\right)=2x^3+9x^2+12x-1$

differentiate with respect to x , we get

$f^{\prime }\left(x\right)=6x^2+18x+12$

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

i.e. $6x^2+18x+12=0$

$6(x^2+3x+2)=0$

$(x+2)(x+1)=0$

$x=-2,x=-1$

Clearly, $f^{\prime }\left(x\right)>0$ if $x<-2\&x>-1$

$f^{\prime }\left(x\right)<0$ if $-2<x<-1$

Thus $f\left(x\right)$ increases in $(-\infty ,-2)\cup (-1,\infty )$, decreases in $(-2,-1)$