#### To determine

**To describe:**

The ways in which a function can fail to be differentiable.

#### Answer

The function is not differentiable at a point if it is not continuous at that point. Also function is not differentiable at points where its graph has sharp corners or vertical tangent.

#### Explanation

a) The function is not differentiable if it is not continuous:

b) The function is not differentiable if f has a corner or kink in it. The graph of f then has no tangent at that point and f is not differentiable:

c) The function is not differentiable if curve has a vertical tangent:

**Conclusion:**

We were able to describe three ways in which a function can fail to be differentiable.