The interval in which $y = x^{2} e^{x}$ is decreasing is.

(- \infty, \infty

)

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(2, 0)

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(2, \infty

)

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(0, 2)

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Solution

The correct option is D $(0, 2)$
$y = x^{2} e^{x}$
$\frac{d y}{d x} = x^{2} e^{x} - 2 x e^{x} = e^{x} (x^{2} - 2 x)$
Now for given function to be decreasing,
$\frac{d y}{d x} < 0 \Rightarrow e^{x} (x^{2} - 2 x) < 0$
$\Rightarrow x (x - 2) < 0 \Rightarrow x \in (0, 2)$

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