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Unit 4: Application of Derivatives

Application of Derivatives Overview

Evaluating a Derivative (Finding the Slope)

Evaluating a Derivative Examples From Actual AP Exams

Identifier: Evaluating a Derivative

Method 1: By Hand

Example 1: By Hand

Example 1: By Hand (Video)

Method 2: Using the Calculator

Example 2: Using the Calculator

Example 2: Using the Calculator (Video)

Finding the Equation of the Tangent Line

Equation of Tangent Line Examples From Actual AP Exams

Identifier: Equation of a Tangent Line

Method: Equation of a Tangent Line

Example 1: Equation of a Tangent Line

Example 1: Equation of a Tangent Line (Video)

Linearization = Tangent Line Approximation = Local Linear Approximation

Tangent Line Approximation Examples from Actual AP Exams

Identifier: Tangent Line Approximation

Method: Tangent Line Approximation

Example 1: Tangent Line Approximation

Example 1: Tangent Line Approximation (Video)

Example 2: Tangent Line Approximation

Example 2: Tangent Line Approximation (Video)

Reading and Sketching the Graphs of f(x), f′ (x), f″(x)

Reading Derivatives Off Graphs Examples from Actual AP Exams

f(x) = y-values of f(x)

f′(x) = slope of f(x)

f″(x) = concavity of f(x)

Identifier: Reading Derivatives Off Graphs

Method: Reading Derivatives Off Graphs

Example 1: Graph the 1st Derivative, f′(x), Given the Graph of f(x).

Example 1: Graph the 1st Derivative, f′(x), Given the Graph of f(x). (Video)

Example 2: Graph the 2nd Derivative, f″(x), Given the Graph of f′(x).

Example 2: Graph the 2nd Derivative, f″(x), Given the Graph of f′(x). (Video)

Example 3: Reading Local Extrema and Intervals of Increasing and Decreasing from f′(x).

Example 3: Reading Local Extrema and Intervals of Increasing and Decreasing from f′(x). (Video)

Physics Relationships

Physics Derivative Examples From Actual AP Exams

Identifier: Physics Relationships

Method: Physics Relationships

Example 1: Physics Relationships

Example 1: Physics Relationships (Video)

Mean Value Theorem

Mean Value Theorem Examples from Actual AP Exams

Identifier: Mean Value Theorem

Method: Mean Value Theorem

Example 1: Mechanical

Example 1: Mechanical (Video)

Example 2: Conceptual

Example 2: Conceptual (Video)

1st Derivative Test: Local Extrema & Increasing/Decreasing Intervals

1st Derivative Test Examples from Actual AP Exams

Identifier: 1st Derivative Test

Method: 1st Derivative Test

Example 1: f′(x) = 0

Example 1: f′(x) = 0 (Video)

Example 2: f′(x) = 0 on Closded Interval [a,b]

Example 2: f′(x) = 0 on Closded Interval [a,b] (Video)

Example 3: f′(x) = 0 and f′(x) = DNE

Example 3: f′(x) = 0 and f′(x) = DNE (Video)

Global Extrema (Absolute Max and Absolute Min)

Absolute Max and Min Examples from Actual AP Exams

Identifier: Global Extrema

Method: Global Extrema

Example 1: Global Extrema

Example 1: Global Extrema (Video)

2nd Derivative Test Option 1: Intervals of Concavity and Inflection Points

2nd Derivative Test Examples From Actual AP Exams

Identifier: 2nd Derivative Test

Method: 2nd Derivative Test

Example f″(x) = 0 IS an Inflection Point.

Example f″(x) = 0 IS an Inflection Point. (Video)

2nd Derivative Test Option 2: Finding Local Max and Local Min

2nd Derivative Test for Local Extrema Examples From Actual AP Exams

Identifier: 2nd Derivative Test

Method: 2nd Derivative Test

Example 1: 2nd Derivative Test

Example 1: 2nd Derivative Test (Video)

Curve Sketching Using the 1st Derivative and 2nd Derivative Tests

Curve Sketching Examples from Actual AP Exams

Identifier: Curve Sketching

Method: Curve Sketching

Example 1: Curve Sketching

Example 1: Curve Sketching (Video)

Optimization Examples from Actual AP Exams

Identifier: Optimization

Method: Optimization

Example 1: Optimization

Example 1: Optimization (Video)

L’Hospital’s Rule

L’Hospital’s Rule Examples from Actual AP Exams

Identifier: L’Hospital’s Rule

Method: L’Hospital’s Rule

Example 1: L’Hospital’s Rule

Example 1: L’Hospital’s Rule (Video)

Example 1: Mechanical (Video)

Unit 4: Application of Derivatives
Mean Value Theorem
Example 1: Mechanical (Video)

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