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  • Please solve RD Sharma class 12 chapter Mean value theorem exercise 14.1 question 1 sub question 1 maths textbook solution

Please solve RD Sharma class 12 chapter Mean value theorem exercise 14.1 question 1 sub question 1 maths textbook solution

Answers (1)

Answer:

Rolle’s Theorem is not applicable

Hint:

f (x)is continuous for al lx and hence continuous in[1,3].

Given:

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

Explanation:

We have

               f (x) = 3 + ( x -2 ) ^ \frac{2}{3}                                                                                                                         …(i)

  1. Being polynomialf (x)is continuous for all x and hence continuous in[1,3].

       2.

              \\f{}' (x) = \frac{2}{3} ( x -2) ^{\frac{2}{3}-1} \\\\ = \frac{2}{3} (x-2 ) ^{\frac{-1}{3}}

            Which exists in (1,3)

           f (x)is derivable in(1,3)

3.

\\f (1) = 3 + ( 1-2) ^{\frac{2}{3}} = 3 + (-1)\frac{2}{3}\\\\ = 3-1 = 2 \\\\ f (3) = 3 + ( 3-2)^\frac{2}{3} = 3 + ( 1) ^\frac{2}{3} \\\\ = 3+1 = 4 \\\\ f (1) \neq f (3 )

Thus, third condition of Rolle’s Theorem is not satisfied.

Hence, Rolle’s Theorem is not applicable.

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