Case 1 :Firstly check the continuity of that function. The function is not differentiable at any point if the function is discontinuous at that point..Because the curve doesn`t exist at the point of discontinuity, so not differentiable at that point.Case 2 :In some specific cases, a function may not be differentiable at the point where the function is continuous. Such points are breaking point.** Breaking points are such points where there is not possible to draw a tangent to the curve at that point .For an example y = |x| is a function which is continuos at (0,0) but not differentiable. For the function y = |x| , (0,0) is a breaking point.** And if you find the left hand limit, L f ` (P) and right hand limit, R f ` (P) of a function f(x) at point P, The function will be differentiable if (i) L f ` (P) and R f ` (P) are defined.(ii) L f ` (P) = R f ` (P) ..Thus, You can also check differentiability of a function using the concept of limit.