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CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 14 of 50
Marks: +1, -0
The function y=x2e−xy=x^2 e^{-x} is decreasing in the interval
Solution:     👈: Video Solution
Explanation: We have,
f(x)=y=x2e−xf(x)=y=x^2 e^{-x}
∴  dydx=2xe−x+x2(−1)e−x=xe−x(2−x)\therefore\;\frac{dy}{dx}=2x e^{-x}+x^2(-1)e^{-x}=x e^{-x}(2-x)
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Now, put   dydx=0\;\frac{dy}{dx}=0
⇒x=0\Rightarrow x=0 and x=2x=2
The points x=0x=0 and x=2x=2 divide the real line into three disjoint intervals i.e., (−∞,0),(0,2)(-\infty,0),(0,2) and (2,∞)(2,\infty)
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