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2. Slope of a Tangent Blank.notebook
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September 07, 2016
Recall: Slope of a Secant (Average Rate of Change)
x
y
1.2 Slope of a Tangent
Recall: Slope of a Tangent (Instantaneous Rate of Change)
x
y
Problem: Tangent line only hits a curve (function) at precisley one point. (Need two points to use difference/quotient formula.
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2. Slope of a Tangent Blank.notebook
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September 07, 2016
Recall: "Estimating" Instantaneous Rate of Change
Ex 1: A) Estimate slope of tangent line for function using difference/quotient method
at
10 8 6 4 2 0 2 4 6 8 10
1098765432
12345678910
x
y
B) Calculate the exact slope of tangent line for function using limits.
at
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2. Slope of a Tangent Blank.notebook
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September 07, 2016
Summary:
Algebraic computation of slopes of tangents using limits. (Instantaneous Rates of Change)
1.
2. Problem with initially setting is you end up with undefined value. (denominator is always equal to zero)
3.Use the point given and leave unknown (do not assign it a really small value )
4. Simplify expression using various rules and methods. (ie: function notation, distribute, factor, reduce rationals etc.)
5.When simplified, substitute to determine the exact slope of tangent.
Limit of diff/quotient formula:
C) Find slope of tangent for at
10 8 6 4 2 0 2 4 6 8 10
1
1
2
3
x
y
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2. Slope of a Tangent Blank.notebook
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September 07, 2016
Homework:
pg 1921
811,15,16,17,21
D) Determine the equation of the tangent line from part C)
Section 1.2 Slope of Tangent
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September 07, 2016
Answers
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