Let $f(x) = \begin{cases} (x-1)\sin\left(\frac{1}{x-1}\right), & x \neq 1 \\ 0, & x = 1 \end{cases}$ …

Mathematics

Problem

Let

f(x) = \begin{cases} (x-1)\sin\left(\frac{1}{x-1}\right), & x \neq 1 \\ 0, & x = 1 \end{cases}

, which of the following statements is true ? (A)

f

is differentiable at

x = 1

but not at

x = 0

(B)

f

is neither differentiable at

x = 0

nor at

x = 1

(C)

f

is differentiable at

x = 0

and at

x = 1

(D)

f

is differentiable at

x = 0

but not at

x = 1