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Provide solution for RD Sharma maths class12 Chapter Maxima and Minima exercise Multiple choice question, question 11.

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Answer: option (d)  None of these.   

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

Given:  f(x)=2\sin 3x+3\cos 3x


We have,

f(x)=2\sin 3x+3\cos 3x

f'(x)=6 \cos 3x-9 \sin 3x                                          

For maxima and minima f'(x)=0

\Rightarrow 6 \cos 3x-9 \sin 3x =0

\Rightarrow 6 \cos 3x=9 \sin 3x

\Rightarrow \frac{\sin 3x}{\cos 3x}=\frac{2}{3}

\Rightarrow \tan 3x=\frac{2}{3}

At x=\frac{5\pi }{6}, \tan 3x=\tan \frac{5\pi }{2}=\tan \frac{\pi}{2} = not defined

So, \tan 3x is not defined\left [\tan 3x\neq \frac{2}{3} \right ]

Thus, x=\frac{5}{6}   is not a critical point.

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