Difference between maximum and minimum values of f(x) = x^4e^ -x^… - Vidyadip

MCQ

Difference between maximum and minimum values of $f(x) = x^4e^{-x^2} \ \ \forall x \in R,$ is -

A
$\frac{4}{e^2} - \frac{2}{e}$
B
$\frac{4}{e} - \frac{2}{e^2}$
✓
$\frac{4}{e^2}$
D
$\frac{2}{e}$

✓

Answer

Correct option: C.

$\frac{4}{e^2}$

c
$f^{\prime}(x)=0$ at $x=0, \pm \sqrt{2}$

$f(\mathrm{x})_{\max }=\frac{4}{\mathrm{e}^{2}} ; f(\mathrm{x})_{\min }=0$

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