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  • Please solve RD Sharma class 12 Chapter Maxima and Minima exercise Multiple choice question, question 34 maths textbook solution.

Please solve RD Sharma class 12 Chapter Maxima and Minima exercise Multiple choice question, question 34 maths textbook solution.

Answers (1)

Answer: (b) \frac{1}{e}

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

Given: y=x^x

Solution:

Let us consider

y=x^x

Applying log on both sides,

\log y=x \log x, (x>0)

On differentiating, we get

\begin{aligned} &\frac{1}{y} \frac{d y}{d x}=1 . \log x+x \cdot \frac{1}{x} \\ &\frac{d y}{d x}=(x)^{x}(1+\log x) \\ &\frac{d y}{d x}=0 \\ &(x)^{x}(1+\log x)=0 \end{aligned}

1+\log x=0

\log x=-1

x=e^{-1}

x=\frac{1}{e}

Therefore, the stationary point is x=\frac{1}{e}

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