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Unformatted text preview: nt to a curve at any given
point
Identify the notation developed
by both Newton and Leibnitz
Practice sketching tangent lines
and estimating slope
Define “derivative” as the limit
as h approaches 0 of
(f(x+h) – f(x))/h and interpret as
the slope of the secant line
approaching the tangent line
Define the derivative as a
function
Sketch the derivative as a new
function with the coordinates
(x,m) in which m is the slope at
any given point x
Sketch the derivative of a
function free hand using critical
points such as “peaks”
Recall various discontinuities of
functions at which the function is
not differentiable: cusps, corners,
jumps, asymptotes and holes NJ CCCS Strands &
Indicators 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 Suggested
Timeframe
(in blocks)
2 2 Course Objective(s)
Present all algebraic properties
of the derivative in relationship
to the original function Student Objectives
•
•
•
• Examine the derivative as
“velocity” •
•
• Apply derivative computation to
trigonometric, exponential,
logarithmic and miscellaneous
functions •
•
•
• Review the “limit” definition of
the derivative
Use the “power rule” to find the
derivative of a function:
f’(x) = nx n1
Apply the Chain Rule when
finding the derivative of a
composition of functions
Apply Product and Quotient
Rules to finding more complex
derivatives
Identify the first derivative as
“instantaneous velocity” and its
connection to “speed”
Identify the second derivative as
acceleration
Distinguish between
instantaneous & average velocity
Practice derivative rules with
trigonometric functions
Review and apply properties of ex
and ln x
Identify the derivatives of
absolute value, greatest integer
and piecewise functions
Apply Chain, Product and
Quotient Rules NJ CCCS Strands &
Indicators Suggested
Timeframe
(in blocks)
6 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 1 4.1
4.2
4.3
4.5 A,B,C
C
A,B,C,D
A,B,C,D,E,F 5 Course Objective(s)
Demonstrate the method of
Implicit Differentiation Student Objectives
• Apply implicit procedures for
differentiating equations of
circles, hyperbolas and ellipses NJ CCCS
4.1
4.2
4.3
4.5 Strands &
Indicators
A,B,C
C
A,B,C,D
A,B,C,D,E,F Suggested
Timeframe
(in blocks)
2 UNIT 4 – Applications of Derivatives
Course Objective(s)
Describe the Extreme Value
Theorem in conjunction
with identifying absolute
and relative extrema on a
given function Student Objectives
•
•
•
•
• Exemplify the Mean Value
Theorem and its Corollary,
Rolle’s Theorem •
• Explain the Extreme Value Theorem
Distinguish between local and absolute
maximums and minimums
Illustrate points or intervals in which
extrema do not exist
Identify functions in which multiple
extrema exist
Define critical values as points in which
a derivative either equals zero or does
not exist
Determine whether the Mean Value
Theorem applies to a given function
Use Rolle’s Theorem to determine
where a derivative is equal to zero NJ CCCS Strands &
Indicators 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 Suggested
Timeframe
(in blocks)
4 1 Course Objective(s)
Establish connections
between a function and its
first and second derivatives Student Objectives
•
•
•
• Sketch curves based on
given information •
•
• Introduce the concept of the
antiderivative •
•
• Use the derivative to...
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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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