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  • Please solve rd sharma class 12 chapter 14 Mean Value Theoram exercise multiple choice question 9 maths textbook solution

Please solve rd sharma class 12 chapter 14 Mean Value Theoram exercise multiple choice question 9 maths textbook solution

Answers (1)

Answer:

Option (d)

Hint:

Find the derivative of f(x) and then apply the mean value theorem.

Given:

f(x)=x(x-2),x\in \left [ 1,2 \right ]

Solution:

             f(x)=x(x-2)

\Rightarrow \; \; \; \; \; f(x)=x^{2}-2x

\Rightarrow \; \; \; \; \; f^{'}(x)=2x-2

\Rightarrow \; \; \; \; \; f^{'}(c)=2c-2

Using mean value theorem,

               f^{'}(c)=\frac{f(b)-f(a)}{b-a}

\Rightarrow \; \; \; \; \; f^{'}(c)=\frac{0-(-1)}{2-1}                                                \left [ \because b=2,a=1 \right ]

\Rightarrow \; \; \; \; \; f^{'}(c)=\frac{1}{1}

\Rightarrow \; \; \; \; \; 2c-2=1                                \Rightarrow \; \; \; \; \; \left [ \because f^{'}(c)=2c-2 \right ]

\Rightarrow \; \; \; \; \; 2c=1+2

\Rightarrow \; \; \; \; \; c=\frac{3}{2}

Hence option (d) is correct.

Posted by

infoexpert26

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