1. Derivatives of Polynomials and Exponential Functions
Section 3.1

3. Power Functions
For n = 4 we find the derivative of f (x) = x4 as follows:

4. Example 1, power rule If f (x) = x6, then f (x) = 6x5.
(b) If y = x1000,
then y = 1000x999.
(c) If y = t 4,
then = 4t 3.
(d) = 3r 2

6. Example 2, differentiate

7. Example 3, Tangent & Normal

8. Example 3, Tangent & Normal
Tangent Line
Normal Line

9. Example 4, constant multiple

11. Example 5, derivative

12. Example 6, horizontal tangent

13. Example 6, horizontal tangent

14. Example 7, Acceleration

16. Example 8
If f (x) = ex – x, find f  and f .

17. 3.1 Derivatives of Polynomials and Exponential Functions
Summarize Notes
Read section 3.1
Homework
Pg.181 #7,9,11,15,19,23,29,34,36,43,44,47,49,51

18. Find the 1st derivative

19. Find the 1st derivative

20. Find the 1st derivative

21. Find the Tangent and Normal lines

22. Find the Tangent and Normal lines

23. Find the Velocity and Acceleration
Find acceleration at 1 second.

24. Find Horizontal Tangents