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.