Question

Prove that the following functions are increasing.
$y=\frac{x^4}{4}-\frac{1}{x}+2$ for x > 0

Answer 1

$y=\frac{x^4}{4}-\frac{1}{x}+2$

$⟹y^{\prime }=x^3+\frac{1}{x^2}$

Here, we see that for $x>0$, $y^{\prime }=\frac{dy}{dx}>0$

Hence , $y$ increases for $x>0$