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  • Explain solution RD Sharma class 12 chapter Maxima and Minima exercise Multiple choice question, question 28 maths

Explain solution RD Sharma class 12 chapter Maxima and Minima exercise Multiple choice question, question 28 maths

Answers (1)

Answer: option(c) \frac{-1}{e}

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

Given: f(x)=x \log _ex

Solution:

We have,

f(x)=x \log _ex

\Rightarrow f'(x)= \log _ex+1

For maxima and minima f'(x)=0

\Rightarrow \log _ex+1=0

\Rightarrow \log _ex=-1

\Rightarrow x=e^{-1}

Now,

f''(x)=\frac{1}{x}

f^{\prime \prime}\left(e^{-1}\right)=\frac{1}{e^{-1}}=e>0

So,x=e^{-1}is the local minima.

Minimum value of  f(x)=f\left(e^{-1}\right)=e^{-1} \log _{e}\left(e^{-1}\right)=-e^{-1}=\frac{-1}{e}

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