AP Calculus Review 3.1-3.5

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AP Calculus Review 3.1-3.5
3.1 Definition(s) of the Derivative
f '(x) 
lim
h 0
f ( x  h)  f ( x)
h
f ' (c ) 
lim
x c
f ( x )  f (c )
xc
Relating f(x) and f’(x) Graphically
3.2 Types of NON-Differentiability
3.2 Types of NON-Differentiability
• Not Continuous
(Remember: Differentiability implies
Continuity)
3.2 Types of NON-Differentiability
• Not Continuous
(Remember: Continuity implies
Differentiability)
• Cusp
3.2 Types of NON-Differentiability
• Not Continuous
(Remember: Continuity implies
Differentiability)
• Cusp
• Corner
3.2 Types of NON-Differentiability
• Not Continuous
(Remember: Continuity implies
Differentiability)
• Cusp
• Corner
• Vertical Tangent
(Note: A vertical tangent is NOT a vertical
asymptote)
3.3 Rules for Differentiation
•Power Rule
• Product Rule
• Quotient Rule
3.4 Rates of Change
• Average Rate of Change
• Motion Problems
3.5 Trig Function Derivatives
• All six trig functions and their derivatives
Workbook Problems
• Lesson 1 #1-4
• Lesson 2 #1-2
• Extra Sheet #5-7 and Examples #1-3
• Lesson 3 #2-4
Review Worksheets
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Worksheet §3.1 ALL (will get on Friday)
Worksheet §3.2 ALL
Worksheet §3.3 #2, 3, 5, 6, 7
Worksheet §3.4 #2-5, 7, 10, 13, 14
Worksheet §3.5 #4-7

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