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  • Please solve RD Sharma class 12 chapter Mean value theorem exercise 14.1 question 1 sub question 5 maths textbook solution

Please solve RD Sharma class 12 chapter Mean value theorem exercise 14.1 question 1 sub question 5 maths textbook solution

Answers (1)

Answer:

Rolle’s Theorem is  applicable [-1,1]

Hint:

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

Given:

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

Explanation:

We have

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

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

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

3. 

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

Thus third condition of Rolle’s Theorem is  satisfied.

Hence, Rolle’s Theorem is  applicable.

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