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  • provide solution for rd sharma maths class 12 chapter 14 Mean Value Theoram exercise multiple choice question 10

provide solution for rd sharma maths class 12 chapter 14 Mean Value Theoram exercise  multiple choice question 10

 

Answers (1)

Answer:

Option (a)

Hint:

Differentiate the given function and then apply Rolle’s Theorem.

Given:

f(x)=x^{3}-3x,x\in \left [ 0,\sqrt{3} \right ]

Solution:

            f(x)=x^{3}-3x,x\in \left [ 0,\sqrt{3} \right ]

            f(x)=x^{3}-3x

\Rightarrow \; \; \; \; \; f^{'}(x)=3x^{2}-3

\Rightarrow \; \; \; \; \; f^{'}(c)=3c^{2}-3

Applying Rolle’s Theorem,

\Rightarrow \; \; \; \; \; f^{'}(c)=0

\Rightarrow \; \; \; \; \; 3c^{2}-3=0

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

\Rightarrow \; \; \; \; \; c^{2}=1

\Rightarrow \; \; \; \; \; c=\pm 1

\Rightarrow \; \; \; \; \; c=1                                   \left [ \because c\in \left [ 0,\sqrt{3} \right ] \right ]

Hence option (a) is correct.

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