Who has the Power?

1. Who has the Power? Today you will investigate the slope of polynomial Parent Graphs and infer an important rule.

2. Warm-Up

3. Tangent Lines • Notice that a tangent to the graph has been drawn at x=1. On the resource page, carefully draw tangents to the curve at x=2, x=4, and x=6 using a straight edge.

4. Tangent Lines • Write a slope statement for (Describe what is happening with the slope.)

5. Tangent Lines • If this graph represented the position of a roller coaster during its first 6 seconds, where was it moving the fastest? • Where was it moving the slowest? • How did you determine your answers?

6. Looking at the slopes graphically • On the resource pages, carefully draw tangents to the curve at x = -3, -2, -1, 0, 1, 2, and 3. • Compare the slopes of the tangent lines you drew to the slope of the tangent that you get by plugging in the x-values into the slope function (computed in warm-up). What do you notice?

7. Derivative of a Constant

8. Positive Integer Powers

9. A function multiplied by a constant

10. Sums and Differences of Functions

11. Let’s Practice Some Given the following expressions for f, find an expression for f ’

13. For which of the following functions can we apply the Power Rule?

14. Use the Power Rule to find

15. Assignment HW A See yutmrrw!