Q. 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]
Explanation
(d)
Given, $f(x) = 2 + (x - 1)^{2/3}$
By using Rolle’s theorem, the given function is not differentiable at $x = 1,$ which cannot satisfy Rolle’s theorem.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.