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  • Need solution for RD Sharma math class class 12 chapter Mean value theorem exercise 14.2  question 2 sub question ii

Need solution for RD Sharma math class class 12 chapter Mean value theorem exercise 14.2 question 2 sub question  (ii)

Answers (1)

Answer:

               c=2 \in(1,3) , Hence, Rolle’s Theorem is verified.

Hint:

f(x)is continuous for all x and hence continuous in [1,3]

 Given:

               f(x)=x^{2}-4 x+3 on [1,3]

Explanation:

We have

               f(x)=x^{2}-4 x+3

  1. Being polynomial f(x) is continuous for all x and hence continuous in [1,3] 
  2. f^{\prime}(x)=2 x-4 , which exists in (1,3) 

            \therefore f (x )is derivable in (1,3) 

       3.

            \\f(1)=(1)^{2}-4(1)+3\\\\ =1-4+3=-3+3=0\\\\ f(3)=(3)^{2}-4(3)+3\)\\\\\ =9-12+3=-3+3=0\\\\ \therefore f(1)=f(3)

Thus all the conditions of Rolle’s Theorem are satisfied.

There exists at least onec \in(1,3)such thatf'(c) = 0

\\ \Rightarrow 2c - 4 = 0 \\\\ \Rightarrow c = 2 \\\\ \Rightarrow c = 2 \in (1,3)

Hence, Rolle’s Theorem is verified.

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