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  • Explain Solution for RD Sharma Maths Class 12 Chapter 17 Maxima and Minima Exercise Fill in the blanks Question 12 maths textbook solution

Explain Solution for RD Sharma Maths Class 12 Chapter 17 Maxima and Minima Exercise Fill in the blanks Question 12 maths textbook solution

Answers (1)

Answer:

              \frac{1}{e}

Hint:

For maxima or minima we must have {f}'\left ( x \right )=0

Given:  f\left ( x \right )=y=xe^{-x}

Solution:

Let y=xe^{-x}

Now differentiate it

\frac{dy}{dx}=e^{-x}-xe^{-x} (product rule)

\frac{dy}{dx}=e^{-x}\left ( 1-x \right )For max/min 

X=1

Hence maximum value of given expression occurs at x=1

\begin{aligned} &y_{\max }=(1) e^{-1}=\frac{1}{e} \\ &y_{\max }=\frac{1}{e} \end{aligned}

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