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

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.