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

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SOLUTION —

Given that, $f(x)=2+(x-1)^{2 / 3}$

By using Rolle's theorem, the given function is not differentiable at $x=1 \in[0,2]$, which cannot satisfy Rolle's theorem

So, The correct option will be (A).

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