JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

Let

f(x)=\left\{\begin{array}{cc}(x-1) \sin \frac{1}{x-1} \text { if } x \neq 1 \\ 0 & \text { if } x=1\end{array}\right.

Then which one of the following is true?

View answer and explanation

Correct option: C

f

is differentiable at

x=0

but not at

x=1

Option C is correct because f(x) is differentiable at x=0 but not at x=1, as the left-hand and right-hand derivatives are not equal at x=1.

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