I have noticed one thing during solving problems : That is, wherever I find a function which is continuous but non differentiable at a point, there has always been some |.|(modulus) function or [.](greatest integer function) in it.
I feel that's the only way one can have a sharp point in the graph of a function. Every other function tend to be smooth at all points.I am unable to manipulate them into a non differentiable continuous function by adding, multiplying, squaring or any other operations.
Is my assumption true ? If not, can you give an example of a function which is continuous but non differentiable at a point except modulus function or GIF function ?