Continuously differentiability of "glued" function I have the following surface for $x,t>0$: $$z(x,t)=\begin{cases}\sin(x-2t)&x\geq 2t\\
(t-\frac{x}{2})^{2}&x<2t \end{cases}$$ How to show that surface is not continuously differentiable along the curve $x=2t$? Truly speaking, I have no idea how to start with this example. Thank you. Andrew

When $x=2t$, what is the value of $\frac x2-t$? of $\cos(x-2t)$? Are these equal?
