#### To determine

**To state: **the numbers with reason at which f is not differentiable

#### Answer

a) f is not differentiable at x = -4, since f is not continuous

b) f is not differentiable at x = -1, since f has corner

c) f is not differentiable at x = 2, since f is not continuous

d) f is not differentiable at x = 5, since f has a vertical tangent

#### Explanation

**1) Concept:**

If f is not continuous or f has corner points or f has vertical tangent at a point, then it is not differentiable at that point.

**2) Calculations:**

From the graph it is clear that f is not differentiable at x = -4 and x = 2 because there is break in curve at those points, means it is not continuous at those points

f is not differentiable at -1 because there is corner at -1

f is not differentiable at 5 also because at 5 there is a vertical tangent.

**Conclusion:**

a) f is not differentiable at x = -4, since f is not continuous

b) f is not differentiable at x = -1, since f has corner

c) f is not differentiable at x = 2, since f is not continuous

d) f is not differentiable at x = 5, since f has a vertical tangent