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Unformatted text preview: identify the
interval over which a function is
increasing, decreasing, or equal to zero
Describe a local maximum as the point
in which the derivative changes from
positive to negative
Describe a local minimum as the point
in which the derivative changes from
negative to positive
Use the second derivative to determine
concavity
Construct sign charts to organize
information about a function and its
derivative
Sketch a function given information
about the derivative or the graph of the
derivative itself
Justify conclusions about the original
function and its extrema using calculus
concepts
Recall the relationships between a
function and the first and second
derivative
Practice using the general formula for
antiderivative: f(x) = x n+1/(n +1)
Apply physics applications (i.e.velocity)
to finding position functions given
initial conditions NJ CCCS Strands &
Indicators Suggested
Timeframe
(in blocks)
3 4.1
4.2
4.3
4.5 A,B,C
C
A,B,C,D
A,B,C,D,E,F 4.1
4.2
4.3
4.5 A,B,C
C
A,B,C,D
A,B,C,D,E,F 3 4.1
4.2
4.3
4.5 A,B,C
C
A,B,C,D
A,B,C,D,E,F 1 Course Objective(s)
Present optimization as an
application of
differentiation Student Objectives
•
• •
Introduce related rates as a
second application of
derivatives • •
•
•
• NJ CCCS Strands &
Indicators Interpret realworld examples in
economics, manufacturing, shipping,
land surveying and marketing
Create equations to minimize or
maximize a value or number of objects,
and apply the concept of “setting the
derivative equal to zero” to identify
maximum and minimum points
Interpret results in the context of the
problem 4.1
4.2
4.3
4.5 A,B,C
A1,A2,C,D,
E
A,B,C,D
A,B,C,D,E,F Identify “common” realworld problems
in which related rates are present: i.e.
ladder sliding down a wall, baseball
player running between bases, hot air
balloon rising, vehicles commuting to
and from various location
Identify all variables in the problem,
and determine the relationship between
them
Recall the Chain Rule and implicit
differentiation
View each variable as dependent with
individual rates
Solve for rates and distances with
appropriate units of measure, and
interpret results 4.1
4.2
4.3
4.5 A,B,C
C
A,B,C,D
A,B,C,D,E,F Suggested
Timeframe
(in blocks)
3 3 UNIT 5 – Integration
Course Objective(s)
Introduce integration by
estimating “area under a
curve” Student Objectives
• •
•
• Describe the indefinite integral
and all associated concepts •
•
• Estimate area using Rectangular
Approximation: Right and Left
Riemann Sums and ‘Midpoint’
Approximation
Estimate area using Trapezoidal
Approximation
Given the actual area, find the error
using the above methods as well as
Simpson’s Rule
Develop and comprehend Riemann’s
summation for actual area: the
number of rectangular subdivisions
approaches infinity and the width of
each rectangle (change in x)
approaches ‘0’
Connect Riemann’s summation to
Leibnitz’s integral notation
Understand all components of the
indefinite integral: limits,
integrand, dx, “+ C”
Describe basic integration in terms
of the “antiderivative” and apply
properties: using constants,
splitting an integral, reversing
limits, etc. NJ CCCS Strands &
Indicators 4.1
4,2
4.3
4.5 A,B,C
A1,A3,C,D,
A,B,C,D
A,B,C,D,E,F 4.1...
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This note was uploaded on 03/12/2010 for the course CALCULUS 1561234586 taught by Professor Zalla during the Spring '10 term at Air Force Institute of Technology, Ohio.
 Spring '10
 Zalla
 Calculus, AP Calculus

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