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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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2nd Derivative Test Examples From Actual AP Exams

  1. Unit 4: Application of Derivatives
  2. 2nd Derivative Test Option 1: Intervals of Concavity and Inflection Points
  3. 2nd Derivative Test Examples From Actual AP Exams

Do you want to see where 2nd Derivative Test 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 Q14
  • 2008 AP Calculus AB MCQ Part A Q17
  • 2008 AP Calculus AB MCQ Part A Q20
  • 2008 AP Calculus AB MCQ Part B Q80
  • 2012 AP Calculus AB MCQ Part B Q80
  • 2013 AP Calculus AB MCQ Part A Q11
  • 2013 AP Calculus AB MCQ Part A Q28
  • 2014 AP Calculus AB MCQ Part A Q19
  • 2014 AP Calculus AB MCQ Part A Q22
  • 2015 AP Calculus AB MCQ Part A Q5
  • 2015 AP Calculus AB MCQ Part A Q13
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