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  • Provide solution for RD Sharma maths class12 Chapter Maxima and Minima exercise Multiple choice question, question 8.

Provide solution for RD Sharma maths class12 Chapter Maxima and Minima exercise Multiple choice question, question 8.

Answers (1)

Answer: option(a) \frac{a+b+c}{3}    

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

Given: f(x)=(x-a)^2+(x-b)^2+(x-c)^2

Solution:

We have,

f(x)=(x-a)^2+(x-b)^2+(x-c)^2

f'(x)=2(x-a)+2(x-b)+2(x-c)
For maxima and minima f'(x)=0

\Rightarrow 2(x-a)+2(x-b)+2(x-c)=0

\Rightarrow 2x-2a+2x-2b+2x-2c=0

\Rightarrow 6x-2a-2b-2c=0

\Rightarrow 6x=2(a+b+c)

\Rightarrow x=\frac{(a+b+c)}{3}

Now,

f''(x)=2+2+2=6>0

So,x=\frac{a+b+c}{3}  is a point of local minima.

Posted by

infoexpert24

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