Question

Find the interval in which the following function is increasing or decreasing.
$f\left(x\right)=x^4-4x^3+4x^2+15$

Answer 1

$f\left(x\right)=x^2-4x^3+4x^2+15$

for increasing / decreasing $f,\left(x\right)\ge 0$

$\therefore f^{\prime }\left(x\right)=4x^3-12x^2+8x$

$=4x(x^2-3x+2)$

$=4x(x-1)(x-2)$

Drawing its sign scheme we have

$\therefore f\left(x\right)$ is increasing in $(0,1)\cup (2,\infty )$

$f\left(x\right)$ is decreasing in $(-\infty ,0)\cup (1,2)$