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  • Please Solve RD Sharma Class 12 Chapter 14 Inverse Trigonometric Function Exercise Fill in the Blanks Question 6 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 14 Inverse Trigonometric Function Exercise Fill in the Blanks Question 6 Maths Textbook Solution.

Answers (1)

Answer:

                c=1

Hint:

Find differentiation of f\left ( x \right ) and then apply Rolle’s Theorem.

Given:

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

Solution:

                f\left ( x \right )=x^{3}-3x

On differentiating we get,

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

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

Applying Rolle’s Theorem,

                {f}'\left ( c \right )=0

\Rightarrow 3c^{2}-3=0        

\Rightarrow c^{2}=1        

\Rightarrow c=\pm 1        

\Rightarrow c= 1                                                                                                                                                  \left [ \because x\: \epsilon \left [ 0,\sqrt{3} \right ] \right ]

 

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