class 12

Math

Calculus

Continuity and Differentiability

Let $f(x)={(x−1)sin(x−11 ),ifx=10,ifx=1}$ . Then which one of the following is true?

- $f$ is neither differentiable at $x=0$ and at $x=1$
- $f$ is differentiable at $x=0$ but not at $x=1$
- f is differentiable at $x=0$ but not at $x=1$
- $f$ is differentiable at $x=1$ but not at $x=0$