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  • Provide solution for RD Sharma maths class12 Chapter Maxima and Minima exercise Multiple choice question, question 10.

Provide solution for RD Sharma maths class12 Chapter Maxima and Minima exercise Multiple choice question, question 10.

Answers (1)

Answer: option(c) 3   

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

Given: f(x)=\sum_{r-1}^{5}(x-r)^2

Solution:

We have,

f(x)=\sum_{r-1}^{5}(x-r)^2

\begin{aligned} &f(x)=(x-1)^{2}+(x-2)^{2}+(x-3)^{2}+(x-4)^{2}+(x-5)^{2} \\ &f^{\prime}(x)=2(x-1+x-2+x-3+x-4+x-5) \\ &f^{\prime}(x)=2(5 x-15) \end{aligned}

For maxima and minima

f'(x)=0

\Rightarrow 2(5x-15)=0

\Rightarrow 5x-15=0

\Rightarrow 5x=15

\Rightarrow x=3

Now,

f''(x)=10>0

So, x =3  is a point of local minima.

Posted by

infoexpert24

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