Question

Find the interval in which the following function is increasing or decreasing.
$f\left(x\right)=2x^3-9x^2+12x-5$

Answer 1

We have,

$f\left(x\right)=2x^3-9x^2+12x-5$

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

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

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

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

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

$x=2,1$

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

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

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

decreases in $(1,2)$.