THanks for ur reply. Can u provide a brief explanation for the non-differentiability of this function?? My major is electrical engineering, and background in analysis is not good.
If you were to graph max(x,y) on, say $\displaystyle -1\le x\le 1$, $\displaystyle -1\le y\le 1$ you would see sharp corners along the lines y= x and y= -x. Generally speaking, only "smooth" functions have derivatives.