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

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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