Q72 / 150 · MHT CET 2020 (12 Oct Shift 1) · Mathematics

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

  • Correct answer
    A
    The function is not differentiable at every point in the $(0,4)$.
  • B
    $f(4) \neq f(0)$
  • C
    Function is not well-defined in the domain.
  • D
    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.

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

Relevant Questions