If $f(x)=|x-2|, x \in[0,4]$ then the Rolle's theorem cannot be applied to the function because

If $f(x)=|x-2|, x \in[0,4]$ then the Rolle's theorem cannot be applied to the function because
  1. The function is not differentiable at every point in the $(0,4)$.
  2. $f(4) \neq f(0)$
  3. Function is not well-defined in the domain.
  4. The function is not continuous at every point in the $[0,4]$.

Solution

Here $f(0)=|0-2|=-2$ and $f(4)=|4-2|=2$ Thus $\mathrm{f}(4) \neq \mathrm{f}(0)$ Hence Rolle's Theorem cannot be applied.

Asked in: MHT CET 2020 (12 Oct Shift 1)

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