CBSE Class 12 Math 2022 Term I Solved Paper - Question 14 | ...

CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 14 of 50

Marks: +1, -0

The function

y=x^2 e^{-x}

is decreasing in the interval

$(0,2)$
$(2, ∞)$
$(-∞, 0)$
$(-∞, 0) ∪(2, ∞)$

Solution:

Explanation: We have,

f(x)=y=x^2 {\e}^{-x}

∴ \;{d y}/{d x}=2 x e^{-x}+x^2(-1) e^{-x}=x e^{-x}(2-x)

Now, put

\;{d y}/{d x}=0

⇒ x=0

and

x=2

The points

x=0

and

x=2

divide the real line into three disjoint intervals i.e.,

(-∞, 0),(0,2)

and

(2, ∞)

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