Let y = x^2 e^ - x , then the interval in which y increases with … - Vidyadip

MCQ

Let $y = {x^2}{e^{ - x}}$, then the interval in which $y $ increases with respect to $x$ is

A
$( - \infty ,\infty )$
B
$( - 2,\,0)$
C
$(2,\infty )$
✓
$(0,\,2)$

✓

Answer

Correct option: D.

$(0,\,2)$

d
(d) $\frac{{dy}}{{dx}} = \frac{{ - 1}}{{{e^x}}}x(x - 2)$ is $ + ve$

when $x(x - 2) $ is $ - ve$

$i.e.,$ $ x$ lies in the interval $x \in (0, 2)$,

exponential function as we know is always $ + ve$.

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