1. 3.2 The Power Rule Thurs Oct 22 Do Now Find the derivative of:

2. Quiz Review Retakes by Tues

3. Computations of Derivatives Thm- For any constant c, Note, when y = c, the slope of that line is always horizontal. Therefore, its derivative must equal 0

4. Thm- Let f(x) = x, then Proof: Note: This means that the derivative of any linear function is equal to the coefficient

5. Power Rule Let’s take a look at the different powers of x. Can you see the pattern in the table? F(x)F’(x) 10 X^11 X^22x X^33x^2 X^44x^3

6. Power Rule cont’d Power Rule - For any real number n, Note: The power rule works for negative exponents, as well as fraction exponents.

7. Ex 3.1 Find the derivatives of

8. Ex 3.2 Find the derivatives of

9. General Derivative Rules Thm- If f(x) and g(x) are differentiable at x and c is any constant, then 1) 2) 3)

10. General Deriv. Rules Remember, to rewrite any expressions so they have exponents! And split the expression into separate terms! You try: Find the derivative of each: 1) 2) 3)

11. Closure Hand in: Find the derivative of: 1) 2) HW: p.139 #7-13 odds, 21-27odds, 33, 49

12. 3.2 Power Rule cont’d Fri Oct 23 Do Now: Find the derivative of: 1) 2)

13. HW Review p.139 #7-13 21- 27, 33, 49 7)-3233) 32s - 24 9) 1/349) a) 11) b) 13) c) 21) 23) 25) 27)

14. Derivative of e^x The derivative of f(x) = e^x is

15. Finding tangent line equations Now that we have the power rule, it is much easier to find the equations of tangent lines. EX: Find the tangent line to the graph at x = 2

16. Differentiability and Continuity If f is differentiable at x = c (the derivative is defined at c) then f is also continuous at c

17. Derivative Info The derivative can tell us when a function is increasing (+), decreasing (-), or horizontal (0) This makes finding the vertex of a function easier

18. Closure Journal Entry: How does the power rule work? What does a derivative tell us about a function? HW: p. 139 #15-19 all, 29 31 43 45

19. 3.2 Power Rule Practice Fri Oct 26 Do Now Find the derivative of the following: 1) 2)

20. HW Review: 139 #15-19, 29 31 43 45 15) y = 32x - 4845) A = f(x) 16) y = -2/125 x + 3/25B = h(x) 17) y = -3x - 32C = g(x) 18) y = 1/12 x + 4/3 19)a) 12e^xb) 25-8e^tc) e^(t-3) 29) 0 31) 43) A - 3, B - 1, C - 2, D - 3

21. Derivative Rules so far: Power Rule E^x Constant Rule Breaking up functions into individual terms

22. Practice Green book worksheet p.184 #5-23

23. Closure Journal Entry: How does the graph of a function relate to the graph of its derivative? HW: Finish worksheet p.184 #5-23

24. HW Review p.184 5-23 odds 5)3x^2 -221) 7)6x23) 9) 0 11) 13) 15) -5x^(-3/2) -2 17) 19)

25. HW Review p.184 5-23 evens 6) 8) 10) -4 12) 14) 16) 18) 20) 22)