# Give an example of a function $f:[-1,1] \rightarrow$ $\mathbb R$ such that $f$ is differentiable at $0$ but not continuous at $0$

Give an example of a function $f:[-1,1] \rightarrow$ $\mathbb R$ such that $f$ is differentiable at $0$ but not continuous at $0$

• I can find examples where the derivative itself is not continuous at 0, but nothing where the function is not continuous at 0. Any thoughts? – km24 Apr 22 '17 at 15:03
• There is no such function. A function must be continuous at a point to be differentiable there. – Chappers Apr 22 '17 at 15:04
• $f$ is differentiable at $x_0 \Rightarrow f$ is continuous at $x_0$ – Itay4 Apr 22 '17 at 15:05
• Are you sure you reported correctly the exercise? It is a very basic and important fact that a function is continuous at all points where it is differentiable. – egreg Apr 22 '17 at 15:06
• I stated the exercise correctly, looks like it turns out to be a trick question! I agree that no such function exists. Glad I wasn't going crazy, haha – km24 Apr 22 '17 at 15:13