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The graphs of f(x), f’(x), f’’(x)

The graphs of f(x), f’(x), f’’(x)

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Ex: Given the Cost and Demand Functions, Maximize Profit

Ex: Given the Cost and Demand Functions, Maximize Profit

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Ex: Find a Demand Function and a Rebate Amount to Maximize Revenue and Profit

Ex: Find a Demand Function and a Rebate Amount to Maximize Revenue and Profit

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Ex 2: Cost Function Applications - Marginal Cost, Average Cost, Minimum Average Cost

Ex 2: Cost Function Applications - Marginal Cost, Average Cost, Minimum Average Cost

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Ex 1: Cost Function Applications - Marginal Cost, Average Cost, Minimum Average Cost

Ex 1: Cost Function Applications - Marginal Cost, Average Cost, Minimum Average Cost

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Ex: Find the Average Cost Function and Minimize the Average Cost

Ex: Find the Average Cost Function and Minimize the Average Cost

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Optimization - Maximize the Area of a Norman Window

Optimization - Maximize the Area of a Norman Window

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Ex: Derivative Application - Minimize the Cost of a Fenced Area - YouTube

Ex: Derivative Application - Minimize the Cost of a Fenced Area - YouTube

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Ex: Derivative Application: Maximize Area - YouTube

Ex: Derivative Application: Maximize Area - YouTube

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Ex: Derivative Application - Maximize Profit - YouTube

Ex: Derivative Application - Maximize Profit - YouTube

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Ex: Optimization - Minimize the Cost to Make a Can with a Fixed Volume

Ex: Optimization - Minimize the Cost to Make a Can with a Fixed Volume

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Ex: Optimization - Minimize the Surface Area of a Box with a Given Volume

Ex: Optimization - Minimize the Surface Area of a Box with a Given Volume

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Ex: Optimization - Maximum Area of a Rectangle Inscribed by a Parabola

Ex: Optimization - Maximum Area of a Rectangle Inscribed by a Parabola

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Ex: Derivative Application - Maximize Profit

Ex: Derivative Application - Maximize Profit

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Ex: Derivative Application - Minimize Cost

Ex: Derivative Application - Minimize Cost

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Ex: Optimization - Maximized a Crop Yield (Calculus Methods)

Ex: Optimization - Maximized a Crop Yield (Calculus Methods)

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Ex 3: Max / Min Application Problem - Derivative Application

Ex 3: Max / Min Application Problem - Derivative Application

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Ex 2: Max / Min Application Problem - Derivative Application

Ex 2: Max / Min Application Problem - Derivative Application

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Ex 1: Max / Min Application Problem - Derivative Application

Ex 1: Max / Min Application Problem - Derivative Application

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Ex 2: Intervals for Which the First and Second Derivative Are Positive and Negative Given a Graph

Ex 2: Intervals for Which the First and Second Derivative Are Positive and Negative Given a Graph

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Ex 1: Intervals for Which the First and Second Derivative Are Positive and Negative Given a Graph

Ex 1: Intervals for Which the First and Second Derivative Are Positive and Negative Given a Graph

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Ex: Determine the Sign of f(x), f'(x), and f''(x) Given a Point on a Graph

Ex: Determine the Sign of f(x), f'(x), and f''(x) Given a Point on a Graph

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Ex 2: Sketch a Function Given Information about Concavity

Ex 2: Sketch a Function Given Information about Concavity

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Ex 1: Sketch a Function Given Information about Concavity

Ex 1: Sketch a Function Given Information about Concavity

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Example: Increasing/Decreasing / Concavity / Relative Extrema / Points of Inflection

Example: Increasing/Decreasing / Concavity / Relative Extrema / Points of Inflection

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The Second Derivative Test using Transcendental Functions

The Second Derivative Test using Transcendental Functions

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Ex: Critical Numbers / Relative Extrema / Second Derivative Test

Ex: Critical Numbers / Relative Extrema / Second Derivative Test

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Ex 2: The Second Derivative Test to Determine Relative Extrema

Ex 2: The Second Derivative Test to Determine Relative Extrema

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Ex 1: The Second Derivative Test to Determine Relative Extrema

Ex 1: The Second Derivative Test to Determine Relative Extrema

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The Second Derivative Test to Determine Relative Extrema

The Second Derivative Test to Determine Relative Extrema

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Ex: Determine Increasing / Decreasing / Concavity by Analyzing the Graph of a Function

Ex: Determine Increasing / Decreasing / Concavity by Analyzing the Graph of a Function

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Ex: Find the Intervals a Function is Increasing/Decreasing/Concave Up or Down - Rational Exponent

Ex: Find the Intervals a Function is Increasing/Decreasing/Concave Up or Down - Rational Exponent

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Ex: Determine Concavity and Points of Inflection - f(x)=x^2*e^(4x)

Ex: Determine Concavity and Points of Inflection - f(x)=x^2*e^(4x)

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Ex: Determine Increasing/Decreasing/Concavity Intervals of a Rational Function

Ex: Determine Increasing/Decreasing/Concavity Intervals of a Rational Function

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Ex: Determine Increasing/Decreasing/Concavity Intervals of a Function

Ex: Determine Increasing/Decreasing/Concavity Intervals of a Function

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Ex: Determine Concavity and Absolute Extrema (Product and Quotient Rule)

Ex: Determine Concavity and Absolute Extrema (Product and Quotient Rule)

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Ex: Concavity of a Degree 5 Polynomial - Irrational Critical Numbers

Ex: Concavity of a Degree 5 Polynomial - Irrational Critical Numbers

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Ex: Determine Concavity and Points of Inflection

Ex: Determine Concavity and Points of Inflection

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Ex: Given the First Derivative, Describe the Function (Incr/Decr/CCU/CCD)

Ex: Given the First Derivative, Describe the Function (Incr/Decr/CCU/CCD)

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Concavity of Transcendental Functions</a> (Additional Examples)

Concavity of Transcendental Functions</a> (Additional Examples)

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Determining the Concavity of a Function

Determining the Concavity of a Function

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Ex: Marginals and Marginal Average Cost

Ex: Marginals and Marginal Average Cost

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Ex: Marginals and Marginal Profit

Ex: Marginals and Marginal Profit

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Marginals

Marginals

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Exponential Decay Models: Part 2

Exponential Decay Models: Part 2

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Exponential Decay Models: Part 1

Exponential Decay Models: Part 1

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Exponential Growth Models Part 2

Exponential Growth Models Part 2

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Exponential Growth Models Part 1

Exponential Growth Models Part 1

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Determine Elasticity of Demand and Unit Elasticity Price (Linear Demand)

Determine Elasticity of Demand and Unit Elasticity Price (Linear Demand)

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Ex: Elasticity of Demand - Quadratic Demand Function

Ex: Elasticity of Demand - Quadratic Demand Function

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Ex: Elasticity of Demand Application Problem

Ex: Elasticity of Demand Application Problem

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Elasticity of Demand: Part 2

Elasticity of Demand: Part 2

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Elasticity of Demand: Part 1

Elasticity of Demand: Part 1

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Ex: Profit Function Application - Maximize Profit

Ex: Profit Function Application - Maximize Profit

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Ex: Profit Function Applications – Average Profit, Marginal Profit, Max Profit

Ex: Profit Function Applications – Average Profit, Marginal Profit, Max Profit

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Ex: Optimization - Maximized a Crop Yield (Calculus Methods)

Ex: Optimization - Maximized a Crop Yield (Calculus Methods)

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Finding Max and Mins Applications: Part 2

Finding Max and Mins Applications: Part 2

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Finding Max and Mins Applications: Part 1

Finding Max and Mins Applications: Part 1

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Ex 2: Sketch a Graph Given Information About a Function's First Derivative

Ex 2: Sketch a Graph Given Information About a Function's First Derivative

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Ex 1: Sketch a Graph Given Information About a Function's First Derivative

Ex 1: Sketch a Graph Given Information About a Function's First Derivative

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Ex 3: Determine Relative Extrema Using The First Derivative Test Involving a Trig Function

Ex 3: Determine Relative Extrema Using The First Derivative Test Involving a Trig Function

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Ex 2: Determine Relative Extrema Using The First Derivative Test Involving a Rational Function

Ex 2: Determine Relative Extrema Using The First Derivative Test Involving a Rational Function

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Ex 1: Determine Relative Extrema Using The First Derivative Test

Ex 1: Determine Relative Extrema Using The First Derivative Test

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Determining Relative Extrema on the Graphing Calculator

Determining Relative Extrema on the Graphing Calculator

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Ex: Critical Numbers / Relative Extrema / First Derivative Test

Ex: Critical Numbers / Relative Extrema / First Derivative Test

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The First Derivative Test to Find Relative Extrema

The First Derivative Test to Find Relative Extrema

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Ex 2: Interpret the Graph of the First Derivative Function - Degree 3

Ex 2: Interpret the Graph of the First Derivative Function - Degree 3

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Ex 1: Interpret the Graph of the First Derivative Function – Degree 2

Ex 1: Interpret the Graph of the First Derivative Function – Degree 2

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Ex 2: First Derivative Concept - Given Information about the First Derivative, Describe the Function

Ex 2: First Derivative Concept - Given Information about the First Derivative, Describe the Function

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Ex 1: First Derivative Concept - Given Information about the First Derivative, Describe the Function

Ex 1: First Derivative Concept - Given Information about the First Derivative, Describe the Function

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Determine where a trig function is increasing/decreasing and relative extrema

Determine where a trig function is increasing/decreasing and relative extrema

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Ex: Find the Intervals Incr/Decr and Relative Extrema (Quad Formula Used)

Ex: Find the Intervals Incr/Decr and Relative Extrema (Quad Formula Used)

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Ex: Find the Intervals Incr/Decr and Relative Extrema Using the First Derivative

Ex: Find the Intervals Incr/Decr and Relative Extrema Using the First Derivative

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Ex: Determine Increasing/Decreasing Intervals and Absolute Extrema (Product Rule)

Ex: Determine Increasing/Decreasing Intervals and Absolute Extrema (Product Rule)

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Ex: Determine Increasing/Decreasing Intervals and Relative Extrema (Product Rule with Exponential)

Ex: Determine Increasing/Decreasing Intervals and Relative Extrema (Product Rule with Exponential)

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Ex: Determine Increasing/Decreasing Intervals and Relative Extrema

Ex: Determine Increasing/Decreasing Intervals and Relative Extrema

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Ex 2: Determine the Intervals for Which a Function is Increasing and Decreasing

Ex 2: Determine the Intervals for Which a Function is Increasing and Decreasing

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Ex 1: Determine the Intervals for Which a Function is Increasing and Decreasing

Ex 1: Determine the Intervals for Which a Function is Increasing and Decreasing

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Ex: Determine Increasing or Decreasing Intervals of a Function

Ex: Determine Increasing or Decreasing Intervals of a Function

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Increasing and Decreasing Functions

Increasing and Decreasing Functions

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Increasing and Decreasing Functions

Increasing and Decreasing Functions

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Ex: Find the Critical Numbers of a Cubic Function

Ex: Find the Critical Numbers of a Cubic Function

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Ex: Find the First and Second Derivative Functions and Function Value (Exponential and Polynomial)

Ex: Find the First and Second Derivative Functions and Function Value (Exponential and Polynomial)

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Ex: Determine the Velocity Function and Acceleration Function from the Position Function

Ex: Determine the Velocity Function and Acceleration Function from the Position Function

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Ex 2: First and Second Derivatives Using the Chain Rule - f(x)=ln(cos(x))

Ex 2: First and Second Derivatives Using the Chain Rule - f(x)=ln(cos(x))

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Ex 1: First and Second Derivatives Using the Chain Rule - f(x)=tan(2x)

Ex 1: First and Second Derivatives Using the Chain Rule - f(x)=tan(2x)

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Ex: Higher Order Derivatives Using the Product Rule

Ex: Higher Order Derivatives Using the Product Rule

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Ex: Find Higher Order Derivatives of Sine

Ex: Find Higher Order Derivatives of Sine

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Ex 6: Determine Higher Order Derivatives Requiring the Quotient Rule

Ex 6: Determine Higher Order Derivatives Requiring the Quotient Rule

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Ex 5: Determine Higher Order Derivatives Requiring the Product Rule and Chain Rule

Ex 5: Determine Higher Order Derivatives Requiring the Product Rule and Chain Rule

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Ex 4: Determine Higher Order Derivatives Requiring the Chain Rule

Ex 4: Determine Higher Order Derivatives Requiring the Chain Rule

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Ex 3: Determine Higher Order Derivatives

Ex 3: Determine Higher Order Derivatives

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Ex 2: Determine Higher Order Derivatives

Ex 2: Determine Higher Order Derivatives

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Ex 1: Determine Higher Order Derivatives

Ex 1: Determine Higher Order Derivatives

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Higher Order Derivatives of Transcendental Functions

Higher Order Derivatives of Transcendental Functions

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Higher-Order Derivatives: Part 2

Higher-Order Derivatives: Part 2

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Higher-Order Derivatives: Part 1

Higher-Order Derivatives: Part 1

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Ex 3: Derivatives of Inverse Trig Functions

Ex 3: Derivatives of Inverse Trig Functions

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Ex 2: Derivatives of Inverse Trig Functions

Ex 2: Derivatives of Inverse Trig Functions

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Ex 1: Derivatives of Inverse Trig Functions

Ex 1: Derivatives of Inverse Trig Functions

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