MHT CET · Maths · Application of Derivatives

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

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 \([0,4]\).

Verified Solution

Answer & Solution

Correct Answer

(A) The function is not differentiable at every point in the \((0,4)\).

Step-by-step Solution

Detailed explanation

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.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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

Step-by-step Solution

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