Question

Determine intervals in which following functions are strictly increasing or strictly decreasing.
$f:R\to R,f\left(x\right)=x^4-4x$.

Answer 1

$f:R\to R$, $f\left(x\right)=x^4-4x$

$f^{\prime }\left(x\right)=4x^3-4$

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

$f\left(x\right)$ is strictly increasing if $f^{\prime }\left(x\right)>0$

$\Rightarrow$ $x>1$ ($\because x^2+x+1>0\forall x\in R)$

$f\left(x\right)$ is strictly decreasing if $f^{\prime }\left(x\right)<0$

$x<1$