1. The Derivative as a Function
Section 2.8

3. Example 1, 1st derivative
If f (x) = x3 – x, find and interpret f ′(x).
Solution:

4. Example 2, 1st derivative
Solution:

5. Example 3, 1st derivative
Solution:

7. Example 4, 2nd derivative
If f (x) = x3 – x, find and interpret f ′′(x).
Solution:
f (x) = x3 – x is f ′(x) = 3x2 – 1.
So the second derivative is

8. Example 4, 3rd derivative
If f (x) = x3 – x, find and interpret f ‘’’(x).
Solution:

9. Example 4, 4th derivative
If f (x) = x3 – x, find and interpret f (4)(x).
Solution:

10. 2.8 The Derivative as a Function
Summarize Notes
Read Section 2.8
Homework
Pg. 162
#21,23,24,27,29,47,48