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

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Applications of Derivatives

Question:

The interval in which $y=x^2 e^{-x}$ is strictly increasing is:

Options:

$(-\infty, \infty)$

$(2, \infty)$

$(-2,0)$

$(0,2)$

Correct Answer:

$(0,2)$

Explanation:

The correct answer is Option (4) → $(0,2)$

$y=x^2 e^{-x}$

so $\frac{dy}{dx}=2xe^{-x}-x^2e^{-x}=0$

so $x(2-x)e^{-x}=0$

$x=0,2$

Using wavy curve method

y is increasing strictly in (0, 2)