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Exploring Polynomial Parent Graphs: Analyzing Tangents and Slopes

Investigate the slopes of polynomial parent graphs, draw tangents, determine roller coaster speed, compare slopes graphically, and practice derivatives of constant powers and functions. Understand the Power Rule.

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Exploring Polynomial Parent Graphs: Analyzing Tangents and Slopes

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Presentation Transcript

  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 ’

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

  13. Use the Power Rule to find

  14. Assignment HW A See yutmrrw!

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