So I've been asked to prove non-differentiability using this particular method, and I'm a bit lost. I'm supposed to prove that $f(x,y) = |x-y|$ is not differentiable along the $x=y$ line. To do it, I'm supposed to use this definition of differentiability:
A function $f$ is called differentiable at a point $a$ in it's domain if there exists a vector $c\in\mathbb{R^{n}}$ such that:
$\lim\limits_{\bf h \to \bf 0} \frac{f(\boldsymbol a + \boldsymbol h) - f(\boldsymbol a) - \boldsymbol c \cdot \boldsymbol h}{|h|} = 0$
Okay, so obviously $c$ would be the gradient of $f$ at that point, and obviously it won't exist because there is an apex there, but I can't for the life of me prove that it doesn't exist. Any help would be appreciated.