1. Differentiability and Piecewise Functions

2. What are the three things that make a function not differentiable ?
Not continuous at the point Vertical tangent line at the point A cusp at the point.

3. Where is the derivative undefined?
1. …at a point of discontinuity.
Example: f(x) is not differentiable at x = ____

4. Where is the derivative undefined?
2. …where there is a vertical tangent line.
Example: y = x1/3 is not differentiable at x = ___

5. 3. …if the graph has a sharp point (cusp)
Where is the derivative undefined?
3. …if the graph has a sharp point (cusp)
f(x) is not differentiable
at x = ____
f(x) is not differentiable
at x = ____

6. Determine the value(s) of x at which the function is not differentiable. Give the reason.

7. Derivatives of piecewise functions…If
then, f ’(x)=
f ’(5)= f ’(-2)=

8. Is the function continuous? Justify your answer.
Is the function differentiable at x = 1? Justify your answer.

9. Determine whether the function is differentiable at x = 3
Determine whether the function is differentiable at x = 3. Justify your answer.

10. Derivatives of Absolute value functions…If
then, f ’(x)=
f ’(5)= f ’(-2)=

11. Is the function differentiable everywhere?