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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
Method 2: Using the Calculator
Example 2: Using the Calculator
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
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 2: Tangent Line Approximation
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 2: Graph the 2nd Derivative, f″(x), Given the Graph of f′(x).
Example 3: Reading Local Extrema and Intervals of Increasing and Decreasing from f′(x).
Physics Relationships
Physics Derivative Examples From Actual AP Exams
Identifier: Physics Relationships
Method: Physics Relationships
Example 1: Physics Relationships
Mean Value Theorem
Mean Value Theorem Examples from Actual AP Exams
Identifier: Mean Value Theorem
Method: Mean Value Theorem
Example 1: Mechanical
Example 2: Conceptual
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 2: f′(x) = 0 on Closded Interval [a,b]
Example 3: f′(x) = 0 and f′(x) = DNE
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
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.
2nd Derivative Test Option 2: Finding Local Max and Local Min
Identifier: 2nd Derivative Test
Method: 2nd Derivative Test
Example 1: 2nd Derivative Test
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
Optimization
Identifier: Optimization
Method: Optimization
Example 1: Optimization
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
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Physics Derivative Examples From Actual AP Exams

  1. Unit 4: Application of Derivatives
  2. Physics Relationships
  3. Physics Derivative Examples From Actual AP Exams

Do you want to see where physics derivative problems appear on previous AP Calc exams and a video solution for those problems?
I have compiled a comprehensive list here so you don’t have to go looking all over the internet.

  • 2008 AP Calculus AB MCQ Part A Q21
  • 2008 AP Calculus AB MCQ Part B Q82
  • 2008 AP Calculus AB MCQ Part B Q86
  • 2012 AP Calculus AB MCQ Part A Q16
  • 2012 AP Calculus AB MCQ Part A Q28
  • 2013 AP Calculus AB MCQ Part A Q8
  • 2013 AP Calculus AB MCQ Part B Q85
  • 2014 AP Calculus AB MCQ Part A Q27
  • 2014 AP Calculus AB MCQ Part B Q90
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