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  • Please solve RD Sharma class 12 Chapter Maxima and Minima exercise Multiple choice question, question 29 maths textbook solution.

Please solve RD Sharma class 12 Chapter Maxima and Minima exercise Multiple choice question, question 29 maths textbook solution.

Answers (1)

Answer: option(a) -128

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

Given: f(x)=2x^3-21x^2+36x-20

Solution:

We have,

f(x)=2x^3-21x^2+36x-20                                                

f'(x)=6x^2-42x+36                           

For maxima and minima f'(x)=0

\Rightarrow 6x^2-42x+36=0

\Rightarrow x^2-7x+6=0

\Rightarrow (x-1)(x-6)=0

\Rightarrow x=1,6

Now,

\begin{aligned} &f^{\prime \prime}(x)=12 x-42 \\ &f^{\prime \prime}(1)=12-42=-30<0 \end{aligned}

So, x = 1 is the local maxima.       

f''(6)=72-42=30>0

So, x = 6 is the local minima.        

f(6)=2(6)^{3}-21(6)^{2}+36(6)-20=432-756+216-20=-128

Posted by

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