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  • provide solution for rd sharma maths class 12 chapter 14 Mean Value Theoram exercise multiple choice question 6

provide solution for rd sharma maths class 12 chapter 14 Mean Value Theoram exercise  multiple choice question 6

Answers (1)

Answer:

option (a) 2

Hint:

Use Rolle’s Theorem formula

Given:

f(x)=2x^{3}-5x^{2}-4x+3,\; x\in \left [ \frac{1}{3},3 \right ]

Solution:

We know that,

        f(x)=ax^{3}+bx^{2}+cx+d,x\in \left [ a,b \right ]

        f(0)=d

        f^{'}(x)=6x^{2}-10x-4

As per Rolle’s Theorem,

        f^{'}(x)=6x^{2}-10x-4

        f^{'}(c)=6c^{2}-10c-4

        f^{'}(c)=0

        \Rightarrow 6c^{2}-10c-4=0

        \Rightarrow 2(3c^{2}-5c-2)=0

        \Rightarrow 3c^{2}-5c-2=0

        \Rightarrow 3c^{2}-6c+c-2=0

        \Rightarrow (3c+1)(c-2)=0

        \Rightarrow c=2,\frac{-1}{3}

        \Rightarrow c=2                                        \left [ \because \frac{-1}{3}\notin \left ( \frac{1}{3},3 \right ) \right ]

Hence, Option (a) is correct.

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