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Ex 4: Implicit Differentiation Involving a Trig Function
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Ex 3: Implicit Differentiation Using the Product Rule and Factoring
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Ex 2: Implicit Differentiation Using the Product Rule
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Ex 1: Implicit Differentiation
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Implicit Differentiation of Equations containing Transcendental Functions
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Implicit Differentiation
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Introduction to Basic Implicit Differentiation - YouTube
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Ex 4: Mean Value Theorem – Quadratic Fomula Needed
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Ex 3: Mean Value Theorem – Rational Function
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Ex 2: Mean Value Theorem – Cubic Function
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Ex 1: Mean Value Theorem – Quadratic Function
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Proof of the Mean Value Theorem
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The Mean Value Theorem
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Ex 2: Rolle's Theorem with Product Rule
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Ex 1: Rolle's Theorem
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Proof of Rolle's Theorem
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Rolle’s Theorem
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Ex: Use Differentials to Approximate Possible Error for the Surface Area of a Sphere
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Ex: Differentials - Approximate Delta y Using dy Using a Sine Function and Find Error Percent
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Ex: Find dy Given a Tangent Function - Requires the Chain Rule
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Ex: Differentials: Compare delta y and dy
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Ex: Using Differentials to Approximate the Value of a Cube Root.
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Ex: Differentials to Approximate Propagated Error and Relative Error
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Ex 2: Differentials: Determine dy given x and dx
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Ex 1: Determine Differential y (dy)
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Differentials
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Ex: Use a Tangent Line to Approximate a Cube Root Function Value – Chain Rule
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Ex: Use a Tangent Line to Approximate a Quotient
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Ex: Use a Tangent Line to Approximate a Square Root Value
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Tangent Line Approximation Given a Function and Derivative Function Value
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Introduction to Differentials
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Ex: Determine Increasing/Decreasing Intervals and Absolute Extrema (Product Rule)
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Ex: Absolute Extrema of a Trigonometric Function on a Closed Interval
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Ex: Absolute Extrema of a Quadratic Function on a Closed Interval
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Ex 2: Absolute Extrema on an Open Interval
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Ex 1: Absolute Extrema on an Closed Interval
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Absolute Extrema of Transcendental Functions
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Absolute Extrema
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The graphs of f(x), f’(x), f’’(x)
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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
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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
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Ex: Find the Average Cost Function and Minimize the Average Cost
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Optimization - Maximize the Area of a Norman Window
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Ex: Derivative Application - Minimize the Cost of a Fenced Area - YouTube
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Ex: Derivative Application: Maximize Area - YouTube
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Ex: Derivative Application - Maximize Profit - YouTube
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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
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Ex: Optimization - Maximum Area of a Rectangle Inscribed by a Parabola
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Ex: Derivative Application - Maximize Profit
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Ex: Derivative Application - Minimize Cost
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Ex: Optimization - Maximized a Crop Yield (Calculus Methods)
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Ex 3: Max / Min Application Problem - Derivative Application
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Ex 2: Max / Min Application Problem - Derivative Application
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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
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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
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Ex 2: Sketch a Function Given Information about Concavity
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Ex 1: Sketch a Function Given Information about Concavity
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Example: Increasing/Decreasing / Concavity / Relative Extrema / Points of Inflection
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The Second Derivative Test using Transcendental Functions
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Ex: Critical Numbers / Relative Extrema / Second Derivative Test
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Ex 2: The Second Derivative Test to Determine Relative Extrema
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Ex 1: The Second Derivative Test to Determine Relative Extrema
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The Second Derivative Test to Determine Relative Extrema
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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
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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
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Ex: Determine Increasing/Decreasing/Concavity Intervals of a Function
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Ex: Determine Concavity and Absolute Extrema (Product and Quotient Rule)
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Ex: Concavity of a Degree 5 Polynomial - Irrational Critical Numbers
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Ex: Determine Concavity and Points of Inflection
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Ex: Given the First Derivative, Describe the Function (Incr/Decr/CCU/CCD)
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Concavity of Transcendental Functions</a> (Additional Examples)
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Determining the Concavity of a Function
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Ex: Marginals and Marginal Average Cost
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Ex: Marginals and Marginal Profit
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Marginals
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Exponential Decay Models: Part 2
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Exponential Decay Models: Part 1
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Exponential Growth Models Part 2
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Exponential Growth Models Part 1
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Determine Elasticity of Demand and Unit Elasticity Price (Linear Demand)
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Ex: Elasticity of Demand - Quadratic Demand Function
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Ex: Elasticity of Demand Application Problem
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Elasticity of Demand: Part 2
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Elasticity of Demand: Part 1
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Ex: Profit Function Application - Maximize Profit
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Ex: Profit Function Applications – Average Profit, Marginal Profit, Max Profit
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Ex: Optimization - Maximized a Crop Yield (Calculus Methods)
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Finding Max and Mins Applications: Part 2
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Finding Max and Mins Applications: Part 1
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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
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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
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