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
