if a function is continuous but non differential at a point it implies

Dear student 

this means that differentiable functions are very atypical among continuous functions. The first known example of a function that is continuous everywhere but differentiable nowhere is the Weierstrass function.

example the absolute value function is actually continuous (though not differentiable) at x=0.

For continuity at a point , the function’s limit tending to that point must exist.Whereas for differentiabilty, limit of change in f(x) divided by change in x when delta x tends to zero must exist . Some functions like I x I is continuous throughout but non-differentiable at x=0