A function $f$ is defined by $f(x)=2+(x-1)^{2 / 3}$ on $[0,2]$. Which of the following is not correct?
Answer & explanation
Correct answer: option 4
We have,
$f(x)=2+(x-1)^{2 / 3} \Rightarrow f^{\prime}(x)=\frac{2}{3(x-1)^{1 / 3}}$
Clearly, $f(x)$ is not differentiable at $x=1$.
So, Rolle's theorem is not applicable on $[0,2]$.