I'm having a hard time trying to understand a theorem of multivariable calculus.
- Statement A = "The partial derivatives of $f$ are continuous in an open set containing (a,b)"
- Statement B = "$f$ is differentiable at (a,b)"
I was wondering why the theorem: A$\implies$B was only true in that way. Why is A$\iff$B false ?
How can a function be differentiable without continuous partial derivatives ? Do you have an example of such a function ?
Thanks a lot for your help and happy new year ;)
Diego, student from Belgium