Let f(x)= array cc (x-1) ( 1 x-1 ), & if x 1 0, & if x=1 array . Then, which one of the…
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
Let \[f(x)=\left\{\begin{array}{cc} (x-1) \sin \left(\frac{1}{x-1}\right), & \text { if } x \neq 1 \\ 0, & \text { if } x=1 \end{array}\right\} .\] Then, which one of the following is true ?
- f is neither differentiable at \(x=0\) nor at \(\mathbf{x}=1\)
- f is differentiable at \(x=0\) and at \(\mathbf{x}=1\)
- f is differentiable at \(x=0\) but not at \(\mathbf{x}=1\)
- f is differentiable at \(\mathbf{x}=1\) but not \(x=0\)
Answer
(B) f is differentiable at x=0 and at x =1
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