Q69 / 155 · WBJEE 2025 · Mathematics

A function $f$ is defined by $f(x)=2+(x-1)^{2 / 3}$ on $[0,2]$. Which of the following statements is incorrect?

A
$f$ is not derivable in $(0,2)$
B
$f$ is continuous in $[0,2]$
C
$f(0)=f(2)$
Correct answer
D
Rolle's theorem is applicable on $[0,2]$

Solution

$f(x)=2+(x-1)^{2 / 3}$ $f(x)$ is not differentiable at $x=1$ Hence Rolle's theorem is not applicable on [0, 2]

Hence, the correct answer is option: 'D'.

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