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  4. The function f given by f(x)=x3 ex is increasing on the interval

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Q. The function $f$ given by $f(x)=x^{3} e^{x}$ is increasing on the interval

KEAMKEAM 2020

Solution:

$f(x)=x^{3} e^{x}$
$f'(x)=e^{x}\left[x^{3}+3 x^{2}\right]$
$f'(x)=0 \Rightarrow x^{2}(x+3)=0$
$\Rightarrow x=0, x=-3$
$(-3, \infty)$