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Applications of Differentiation

Applications of Differentiation

Eddie Woo via YouTube Direct link

Finding Stationary Points

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Finding Stationary Points

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Applications of Differentiation

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

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