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  • Please solve RD Sharma class 12 Chapter Maxima and Minima exercise Multiple choice question, question 33 maths textbook solution.

Please solve RD Sharma class 12 Chapter Maxima and Minima exercise Multiple choice question, question 33 maths textbook solution.

Answers (1)

Answer: ( c) e^{\frac{1}{e}}

Hint: For local maxima or minima, we must have f'(x)=0.

Given: f(x)=\left (\frac{1}{x} \right )^x

Solution:

We have,

f(x)=\left (\frac{1}{x} \right )^x  

f^{\prime}(x)=\left(\frac{1}{x}\right)^{x}\left(\log \left(\frac{1}{x}\right)-1\right)

For maxima and minima f'(x)=0

\Rightarrow \left(\frac{1}{x}\right)^{x}\left(\log \left(\frac{1}{x}\right)-1\right)=0           

\log 1- \log x=1

\frac{1}{x}=e

x=\frac{1}{e}

Posted by

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