Unit 6: Curve Sketching
Date: _
Lesson#1: Increasing & Decreasing Functions
L.G.: I can determine the intervals of increase and decrease of a function by examining its first derivative.
Intervals of Increase and Decrease
A function is increasing in an int
Unit II - Derivatives
Date: _
Lesson #1: Finding the Instantaneous Rates of Change by First Principles
L.G.: I can determine the instantaneous rate of change of a function by first principles and prove that a function is
differentiable.
Recall: Using the
Unit I: Intro to Calculus
Date:_
Lesson #1: Average and Instantaneous Rates of Change
L.G.: I can calculate the average and instantaneous rate of change of a function and interpret these values
as the slope of the secant and tangent respectively.
Minds On
Unit II - Derivatives
Date: _
Lesson #2: Derivatives of Functions Short Cuts - The Power Rule
L.G. : I can determine and justify the derivative of a function by applying the Power Rule.
Recall the Derivative of a Function
So far, we have seen that the ins
Unit VI: Curve Sketching
Date: _
Lesson #2: Maximum and Minimum Values
L.G.: I can determine the absolute and local max/min values of a function using the first derivative.
Critical numbers and Critical Points
The point at which the tangent line is horizo
Unit I: Intro to Calculus
Date: _
Lesson 2: The Limiting of a Function
L.G. : I can determine the limit of a function using appropriate techniques.
Definition of a Limit
What happens to the value of a function f, as x gets closer and closer to a particula
Unit II - Derivatives
Date: _
Lesson #3: The Chain Rule
L.G.: I can identify composite functions and differentiate them using the chain rule.
Recall: Composite Functions
2 x 1 determine the following:
Given f ( x) x 2 , g ( x) x 2 and h( x)
( g f )( 3)
(
Unit I: Intro to Calculus
Date: _
Lesson #3: Properties of Limits
L.G.: I can use the properties of limits to determine the limit of composite functions.
Side Note Radical Expressions
Often times in math, we simplify radical expressions that appear in the
Curve Sketching
Date: _
Lesson #3: Analyzing Concavity (Curvature)
L.G.: I can determine the concavity (curvature) of the graph of a function by analyzing the second derivative.
Definition of Concavity
The graph of y f (x) is concave up on an interval if
Unit II - Derivatives
Date: _
Lesson #5: The Quotient Rule
L.G.: I can differentiate a rational function using the quotient rule.
The Quotient Rule
Given a rational function defined by
the first derivative of
is given by
Proof: Let
Example1: Determine the