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Finding Stationary Points
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Classroom Contents
Applications of Differentiation
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- 1 Finding Stationary Points
- 2 Non-Turning Stationary Points
- 3 Average Speed & Velocity
- 4 Equations of Motion
- 5 Instantaneous Speed & Velocity
- 6 Motion Notation
- 7 Motion Terminology
- 8 Prologue to Motion
- 9 Acceleration
- 10 Describing Motion
- 11 Motion Notation - Quick Note
- 12 Tricky Tangent Question (1 of 2)
- 13 Tricky Tangent Question (2 of 2)
- 14 Thomas & Henry Question (1 of 2)
- 15 Thomas & Henry Question (2 of 2)
- 16 Introduction to Max/Min Problems (1 of 2)
- 17 Introduction to Max/Min Problems (2 of 2)
- 18 Max/Min Problem Solving Steps: The 3 Cs
- 19 Max/Min: Squares of Two Numbers (1 of 3)
- 20 Max/Min: Squares of Two Numbers (2 of 3)
- 21 Max/Min: Squares of Two Numbers (3 of 3)
- 22 Max/Min: The A4 Box (1 of 2)
- 23 Max/Min: The A4 Box (2 of 2)
- 24 Max/Min: Rowing/Walking Problem (1 of 2)
- 25 Max/Min: Rowing/Walking Problem (2 of 2)
- 26 Max/Min: Rectangle Inscribed in Scalene Triangle (1 of 2)
- 27 Max/Min: Rectangle Inscribed in Scalene Triangle (2 of 2)
- 28 Max/Min: Two Cars Approaching An Intersection (1 of 2)
- 29 Max/Min: Two Cars Approaching An Intersection (2 of 2)
- 30 Second Derivative & Implications for Graphs
- 31 Applications of Differentiating Trigonometric Functions (alternative method for example question)
- 32 Applications of Differentiating Trigonometric Functions (example question)
- 33 Introduction to Straight Line Motion: The Tennis Ball
- 34 Investigating the Tennis Ball with Calculus
- 35 Language for Describing Straight Line Motion
- 36 Overview of All HSC Motion Topics
- 37 Straight Line Motion: introductory example question
- 38 Geometrical Applications of Calculus (1 of 4: An Introduction to the applications of calculus)
- 39 Geometrical Applications of Calculus (2 of 4: Increasing, Decreasing or Stationary Points)
- 40 Geometrical Applications of Calculus (3 of 4: Some Introductory Examples)
- 41 Geometrical Applications of Calculus (4 of 4: Using the derivative for stationary points of a graph)
- 42 Exploring Stationary Points (1 of 3: In Depth Introduction to Stationary Points)
- 43 Increasing & Decreasing (1 of 1: Harder Examples)
- 44 Exploring Stationary Points (2 of 3: Introductory Examples regarding nature of Stationary Points)
- 45 Exploring Stationary Points (3 of 3: Principles for Choosing Values to Test for Stationary Points)
- 46 The Second Derivative (1 of 3: Introducing Terminology)
- 47 The Second Derivative (2 of 3: Explaining dx²)
- 48 The Second Derivative (3 of 3: Using the Product Rule to Prove Theorems)
- 49 Geometry of the Second Derivative (1 of 4: Reviewing the Derivative)
- 50 Geometry of the Second Derivative (2 of 4: Graphical correspondence of original and its derivatives)
- 51 Geometry of the Second Derivative (3 of 4: Finding the concavity of a circle)
- 52 Geometry of the Second Derivative (4 of 4: Why does the Derivative Graphs correlate?)
- 53 Using the Second Derivative (1 of 5: Finding the Point of Inflexion)
- 54 Using the Second Derivative (2 of 5: Turning Point vs Stationary Point analogy)
- 55 Using the Second Derivative (3 of 5: Why the Points of Inflexion may not exist when f"(x) = 0)
- 56 Using the Second Derivative (4 of 5: Examples where f"(x)=0 doesn't mean Point of Inflexion)
- 57 Using the Second Derivative (5 of 5: Where the concavity changes but f"(x) doesn't exist)
- 58 Points of Inflexion: Step-by-Step Guide
- 59 Stationary Points: Step-by-Step Guide
- 60 Graphing Derivatives (1 of 4: Graphing the Derivative functions from the original function)
- 61 Graphing Derivatives (2 of 4: Using the Derivative function to determine the original function)
- 62 Graphing Derivatives (3 of 4: Process to graphically find the primitive)
- 63 Graphing Derivatives (4 of 4: Harder Derivatives [Discontinuous Functions])
- 64 Curve Sketching with Calculus (1 of 3: Using Calculus to find the Stationary Points)
- 65 Curve Sketching with Calculus (2 of 3: Finding Intercepts and Regions to assist Curve Sketching)
- 66 Curve Sketching with Calculus (3 of 3: Using the Stationary Points to assist with Curve Sketching)
- 67 Max/Min Problems (1 of 3: Introduction to Optimisation)
- 68 Max/Min Problems (2 of 3: Using a Table of Values to Determine Absolute Maxs/Mins)
- 69 Max/Min Problems (3 of 3: Finding the Maximum point of more complex equations)
- 70 Optimisation (1 of 3: Setting up equations to "optimise" for max volume)
- 71 Max/Min Distance Problems (1 of 4: Introducing a Parameter to solve Max/Min Problems)
- 72 Max/Min Distance Problems (2 of 4: Discussing Restrictions on Max/Min Distance Problems )
- 73 Optimisation (2 of 3: Using the Derivative to find possible turning points)
- 74 Optimisation (3 of 3: Finding the Hidden Conditions and Solving the Problem)
- 75 Max/Min Distance Problems (3 of 4: A Plausible real world problem)
- 76 Max/Min Distance Problems (4 of 4: Why is it not essential to test nature of T.P. in this scenario)
- 77 Equations of Tangents & Normals
- 78 Understanding Stationary Points (1 of 3: Classifications)
- 79 Understanding Stationary Points (2 of 3: Location)
- 80 Understanding Stationary Points (3 of 3: Determining nature)
- 81 Critical Values (1 of 2: Piecemeal functions)
- 82 Critical Values (2 of 2: Cusps)
- 83 Graphing Stationary Points (1 of 3: Using the first derivative)
- 84 Graphing Stationary Points (2 of 3: Notation of the second derivative)
- 85 Graphing Stationary Points (3 of 3: Visualising the second derivative)
- 86 Using the Second Derivative (1 of 2: Locating stationary points)
- 87 Using the Second Derivative (2 of 2: Determining nature of stationary points)
- 88 Flowchart for Testing Stationary Points
- 89 Points of Inflexion (1 of 2: Understanding & identifying)
- 90 Points of Inflexion (2 of 2: Discontinuities in the second derivative)
- 91 Mathematics Ext 1 Exam Questions (4 of 4: Stationary points)
- 92 Absolute Maximum/Minimum (1 of 2: Domain restricted polynomial)
- 93 Absolute Maximum/Minimum (2 of 2: Unusual rational function)
- 94 Applications of Maximisation/Minimisation (1 of 2: Largest rectangle area question)
- 95 Applications of Maximisation/Minimisation (2 of 2: Interpreting the calculus)
- 96 Max/Min in Geometry (1 of 3: General principles)
- 97 Max/Min in Geometry (2 of 3: Cylinder in a cone)
- 98 Max/Min in Geometry (3 of 3: Applying calculus)
- 99 Interpreting a Graph w/ Calculus (1 of 2: Sketching the curve)
- 100 Using Derivatives of Trigonometric Functions (2 of 2: Sketching a curve)
- 101 Tricky Max/Min Question: Finding the Derivative
- 102 Tricky Max/Min Question: Solving for Stationary Points
- 103 Using Calculus to Graph y = x – e^x
- 104 Graphing Log Function with Calculus (1 of 3: Finding Domain and Derivative)
- 105 Graphing Log Function with Calculus (2 of 3: Understanding the Derivative)
- 106 Graphing Log Function with Calculus (3 of 3: Sketching the Curve)
- 107 Sign of the Derivative (7 of 7: Determining nature of stationary points)
- 108 Sign of the Derivative (6 of 7: Locating stationary points)
- 109 Sign of the Derivative (5 of 7: Distinguishing stationary points)
- 110 Sign of the Derivative (4 of 7: Vertical tangent)
- 111 Sign of the Derivative (3 of 7: Basic worked example)
- 112 Sign of the Derivative (2 of 7: Increasing, stationary, decreasing)
- 113 Sign of the Derivative (1 of 7: Differentiation review questions)
- 114 Classifying Stationary Points (1 of 3: Review of point types)
- 115 Classifying Stationary Points (2 of 3: Flowchart for locating points)
- 116 Classifying Stationary Points (3 of 3: Flowchart for determining nature)
- 117 Determine Function from Stationary Points
- 118 The Second Derivative (1 of 3: Investigating a pandemic curve)
- 119 The Second Derivative (2 of 3: Exploring first derivative values)
- 120 The Second Derivative (3 of 3: Notation)
- 121 Geometry of the Derivatives (1 of 6: Review question)
- 122 Geometry of the Derivatives (2 of 6: Exploring gradient & concavity)
- 123 Geometry of the Derivatives (3 of 6: Points of inflexion)
- 124 Geometry of the Derivatives (4 of 6: Determining max/min with second derivative)
- 125 Geometry of the Derivatives (5 of 6: What if the second derivative equals 0?)
- 126 Geometry of the Derivatives (6 of 6: How do I choose which derivative to use?)
- 127 Identifying Important Points with Calculus (worked solution)
- 128 What is Optimisation? (1 of 6: Review questions)
- 129 What is Optimisation? (2 of 6: The barbecue scenario)
- 130 What is Optimisation? (3 of 6: Example derivative)
- 131 What is Optimisation? (4 of 6: Checking endpoints)
- 132 What is Optimisation? (5 of 6: Constructing a model)
- 133 What is Optimisation? (6 of 6: Finding the minimum)
- 134 Derivatives of Motion (1 of 3: What does each derivative signify?)
- 135 Derivatives of Motion (3 of 3: Understanding movement)
- 136 Derivatives of Motion (2 of 3: Graphs for displacement, velocity & acceleration)
- 137 Interpreting Motion Graphically (1 of 4: Direction of movement)
- 138 Interpreting Motion Graphically (2 of 4: Identifying specific features)
- 139 Interpreting Motion Graphically (3 of 4: Exploring acceleration)
- 140 Interpreting Motion Graphically (4 of 4: Velocity & acceleration graphs)