A function which is differentiable in an interval , it is also continuous in that interval.
But a function which is continuous in an interval, is not necessarily differentiable in that interval.
For example, the modulus function l x l is continuous in its domain but it is not differentiable at x = 0 .
Plotting the graph of of l x l , we observe that there is a sharp angular point at x = 0.
Hence we write in general that a function is not differentiable at a point where the graph has an angular point.
It is because the slope of the graph (derivative) changes across this point.