derivate of a piecewise function $f(x)$ at$ x=0$. There is a piecewise function $f(x)$
$$f(x)= \begin{cases} 1 ,\ \ \text{if}\ \  x \geq \ 0 \\ 0,\ \  \text{if}\ \  x<0 \end{cases}$$ 
what is the derivative of the $f(x)$ at $x=0$?
Is it $0$? Or since it is not continuous, the derivative does not exists? 

Another way you can prove that your function is not differentiable at a=0 is to show that the left hand limit and the right hand limit in the definition of f'(a) are not equal. When you take h approaching 0 from the left, f'(0) is infinite. When you take h approaching 0 from the right, f'(0)=0. Since the left hand and right hand limits are not equal, f'(0) does not exist. 
