Section 2.1The Tangent and Velocity Problems

AP CalculusSeptember 10, 2009Berkley High School, D2B2

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The importance of slope

Imagine we are going to model an everyday phenomenon like motion.

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The importance of slope

Imagine we are going to model some everyday phenomenon like motion.

We’ll start with an easy example:

“A randomly selected calculus teacher enters I-75 at exit 62 (11 Mile Road). He heads north at a speed of 65 miles per hour.” Make an equation that shows mile mark to traveled to (M) as a function of hours (H) traveled.

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The importance of slope

6265 HM

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The importance of slope

In this function, what does slope represent?

In a position equation, the slope represents “velocity.”

6265 HM

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Graph it.

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What if?

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Can we find the slope/velocity?

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Using secant line as approximation of slope, from (0, 0) to (2.5, 150)

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Using secant line as approximation of slope, from (0, 0) to (2.5, 150)

150 060

2.5 0m

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Using secant line as approximation of slope. From (2, 136) to (2.5, 150)

2825.2

136150

m

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Approximation of slope, from (2.25, 144) to (2.5, 150)

2425.25.2

144150

m

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Using Y= and Tables

If you feel comfortable with finding slope by hand, you might consider using the calculator’s ability to do many calculations simultaneously.

Demonstration…

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Using Y= and Lists

Step 1: Put the function in question in Y=

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Using Y= and Lists

Step 2: Put sample X value in a list

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Using Y= and Lists

Step 3: Put as the header to a different the slope formula

1

1112 5.2

)()5.2(

L

LYYL

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Assignment

Section 2.1, Exercises 1-9 odd