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

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Presentation transcript:

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

Warm-Up Each team member should compute one of these derivatives using the IROC method.

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.

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

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?

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?

Derivative of a Constant

Positive Integer Powers

A function multiplied by a constant

Sums and Differences of Functions

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

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

Use the Power Rule to find

Assignment HW A See yu tmrrw!