The interval in which the function x^2 e^ - x is non decreasing, … - Vidyadip

MCQ

The interval in which the function ${x^2}{e^{ - x}}$ is non decreasing, is

A
$( - \infty ,\,\,2]$
✓
$[0, 2]$
C
$[2,\,\,\infty )$
D
None of these

✓

Answer

Correct option: B.

$[0, 2]$

b
(b) Let $y = f(x) = {x^2}{e^{ - x}}$

==> $\frac{{dy}}{{dx}} = 2x{e^{ - x}} - {x^2}{e^{ - x}} = {e^{ - x}}(2x - {x^2})$

Hence $f'(x) \ge 0$ for every $x \in [0,\,2]$

therefore it is non-decreasing in $ [0,2].$

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