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  • Need solution for RD Sharma maths class 12 chapter Maxima and Minima exercise Multiple Choice question, question 18.

Need solution for RD Sharma maths class 12 chapter Maxima and Minima exercise Multiple Choice question, question 18.

Answers (1)

Answer: option(c) \frac{\pi}{6}

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

Given: f(x)=\sin x+\sqrt{3}\cos x

Solution:

We have,

f(x)=\sin x+\sqrt{3}\cos x

f'(x)=\cos x-\sqrt{3}\sin x                                             

For maxima and minima  f'(x)=0

\Rightarrow \cos x-\sqrt{3}\sin x=0

\Rightarrow \cos x=\sqrt{3}\sin x

\Rightarrow \tan x=\frac{1}{\sqrt{3}}

\Rightarrow x =\frac{\pi}{6}

Now,

\begin{aligned} &f^{\prime \prime}(x)=-\sin x-\sqrt{3} \cos x \\ &f^{\prime \prime}\left(\frac{\pi}{6}\right)=-\sin \left(\frac{\pi}{6}\right)-\sqrt{3} \cos \left(\frac{\pi}{6}\right) \\ &f^{\prime \prime}\left(\frac{\pi}{6}\right)=-\frac{1}{2}-\frac{3}{2}=-2<0 \end{aligned}

So x=\frac{\pi}{6} is local maxima.

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