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  • Please Solve RD Sharma Class 12 Chapter 14 Inverse Trigonometric Function Exercise Fill in the Blanks Question 2 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 14 Inverse Trigonometric Function Exercise Fill in the Blanks Question 2 Maths Textbook Solution.

Answers (1)

Answer:

                0

Hint:

Find differentiation of and then apply mean value theorem.

Given:

                f\left ( x \right )=8x^{2}-7x+5,x\: \epsilon \left [ -6,6 \right ]

Solution:

                f\left ( x \right )=8x^{2}-7x+5

On differentiating we get,

\Rightarrow {f}'\left ( x \right )=16x-7        

\Rightarrow {f}'\left ( c \right )=16c-7        

Apply mean value theorem,

                \begin{aligned} & f^{\prime}(c)=\frac{f(b)-f(a)}{b-a} \\\\ \Rightarrow & 16 c-7=\frac{288-42+5-(288+42+5)}{6+6} \\\\ \Rightarrow & 16 c-7=\frac{251-335}{12} \\\\ \Rightarrow & 16 c-7=\frac{-84}{12} \\\\ \Rightarrow & 16 c-7=-7 \end{aligned}

                \Rightarrow 16c=0

                \Rightarrow c=0

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