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

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

Answers (1)

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

Solution:

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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