Mathematics I: MAS 116

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Mathematics I MAS 116

• Week 9 6 August 2004

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Announcements
1. There is no weekly quiz this week. 2. The
grade for the mid-term will be announced soon!
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Weekly Outline

• Absolute Maxima and Minima
• Applied Maximum and Minimum Problems
• Rolles Theorem Mean Value Theorem
• The Indefinite Integral Integral Curves

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Absolute Maxima and Minima
absolute maximum
relative maximum
relative minimum
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
closed
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Absolute Maxima and Minima
open
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Absolute Maxima and Minima
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Absolute Maxima and Minima
end point
end point
critical point
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Absolute Maxima and Minima
end point
end point
critical points
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Absolute Maxima and Minima
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Applied Maximum and Minimum Problem
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Applied Maximum and Minimum Problem
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Applied Maximum and Minimum Problem
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Applied Maximum and Minimum Problem
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Applied Maximum and Minimum Problem
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Applied Maximum and Minimum Problem
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Applied Maximum and Minimum Problem
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Applied Maximum and Minimum Problem
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Applied Maximum and Minimum Problem
r
h
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Applied Maximum and Minimum Problem
r
h
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Applied Maximum and Minimum Problem
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Applied Maximum and Minimum Problem
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Applied Maximum and Minimum Problem
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Applied Maximum and Minimum Problem
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Rolles Theorem Mean-value Theorem
a
a
b
b
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Rolles Theorem Mean-value Theorem
a
b
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Rolles Theorem Mean-value Theorem
a
b
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Indefinite Integrals
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Indefinite Integrals
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Indefinite Integrals
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Indefinite Integrals
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Indefinite Integrals
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Indefinite Integrals
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Indefinite Integrals
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Indefinite Integrals
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Indefinite Integrals Integral Curves
F(x)
C 6
C 4
C 2
C 0
x
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Indefinite Integrals Integral Curves
F(x)
C 6
C 4
C 2
C 0
x
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Indefinite Integrals Integral Curves
F(x)
C 6
C 4
C 2
C 0
x
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Indefinite Integrals Differential Equation
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Indefinite Integrals Differential Equation
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Indefinite Integrals Differential Equation
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Indefinite Integrals Differential Equation