Question

A function $ f $ is defined by $ f(x ) = 2 + (x - 1)^{2/3} $ in $ [0, 2] $ . Which of the following is not correct ?

• A. $ f $ is not derivable in $ (0, 2) $
• B. $ f $ is continuous in $ [0, 2] $
• C. $ f (0) = f (2) $
• D. Rolle’s theorem is true in $ [0, 2] $

Answer 1

Answer: (D)

Rolle’s theorem satisfies the following conditions
(a) It is continuous in the closed interval.
(b) It is differentiable in the open interval.
(c) $f(a) = f(b)$
Given that, $f( x ) = 2 + (x-1)^2/3$
By using Rolle’s theorem, the given function is not differentiable at $(0, 2)$, which cannot satisfy Rolle’s theorem.