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Provide solution for rd sharma maths class 12 chapter 16 Increasing and decreasing functions exercise multiple choice quection, question 11

Answers (1)

Correct option (b)

Hint: If f(x)  is increasing function {f}'(x)>0

Given: f(x)=x^{2} e^{-x}

Explanation: It is given that

 f(x)=x^{2} e^{-x}

Differentiate (i) w.r.t  x

 \begin{aligned} &f^{\prime}(x)=-x^{2} e^{-x}+x e^{-x} \\ &f^{\prime}(x)=-e^{-x} x(x-2) \end{aligned}

f(x) is monotonically increasing,{f}'(x)>0

\begin{aligned} &-e^{-x} x(x-2)>0 \\ &x(x-2)>0 \end{aligned}

So, 0<x<2

Thus, f(x) is monotonically increasing 0<x<2

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