Applications of Differentiation

Finding Stationary Points.
Non-Turning Stationary Points.
Average Speed & Velocity.
Equations of Motion.
Instantaneous Speed & Velocity.
Motion Notation.
Motion Terminology.
Prologue to Motion.
Acceleration.
Describing Motion.
Motion Notation - Quick Note.
Tricky Tangent Question (1 of 2).
Tricky Tangent Question (2 of 2).
Thomas & Henry Question (1 of 2).
Thomas & Henry Question (2 of 2).
Introduction to Max/Min Problems (1 of 2).
Introduction to Max/Min Problems (2 of 2).
Max/Min Problem Solving Steps: The 3 Cs.
Max/Min: Squares of Two Numbers (1 of 3).
Max/Min: Squares of Two Numbers (2 of 3).
Max/Min: Squares of Two Numbers (3 of 3).
Max/Min: The A4 Box (1 of 2).
Max/Min: The A4 Box (2 of 2).
Max/Min: Rowing/Walking Problem (1 of 2).
Max/Min: Rowing/Walking Problem (2 of 2).
Max/Min: Rectangle Inscribed in Scalene Triangle (1 of 2).
Max/Min: Rectangle Inscribed in Scalene Triangle (2 of 2).
Max/Min: Two Cars Approaching An Intersection (1 of 2).
Max/Min: Two Cars Approaching An Intersection (2 of 2).
Second Derivative & Implications for Graphs.
Applications of Differentiating Trigonometric Functions (alternative method for example question).
Applications of Differentiating Trigonometric Functions (example question).
Introduction to Straight Line Motion: The Tennis Ball.
Investigating the Tennis Ball with Calculus.
Language for Describing Straight Line Motion.
Overview of All HSC Motion Topics.
Straight Line Motion: introductory example question.
Geometrical Applications of Calculus (1 of 4: An Introduction to the applications of calculus).
Geometrical Applications of Calculus (2 of 4: Increasing, Decreasing or Stationary Points).
Geometrical Applications of Calculus (3 of 4: Some Introductory Examples).
Geometrical Applications of Calculus (4 of 4: Using the derivative for stationary points of a graph).
Exploring Stationary Points (1 of 3: In Depth Introduction to Stationary Points).
Increasing & Decreasing (1 of 1: Harder Examples).
Exploring Stationary Points (2 of 3: Introductory Examples regarding nature of Stationary Points).
Exploring Stationary Points (3 of 3: Principles for Choosing Values to Test for Stationary Points).
The Second Derivative (1 of 3: Introducing Terminology).
The Second Derivative (2 of 3: Explaining dx²).
The Second Derivative (3 of 3: Using the Product Rule to Prove Theorems).
Geometry of the Second Derivative (1 of 4: Reviewing the Derivative).
Geometry of the Second Derivative (2 of 4: Graphical correspondence of original and its derivatives).
Geometry of the Second Derivative (3 of 4: Finding the concavity of a circle).
Geometry of the Second Derivative (4 of 4: Why does the Derivative Graphs correlate?).
Using the Second Derivative (1 of 5: Finding the Point of Inflexion).
Using the Second Derivative (2 of 5: Turning Point vs Stationary Point analogy).
Using the Second Derivative (3 of 5: Why the Points of Inflexion may not exist when f"(x) = 0).
Using the Second Derivative (4 of 5: Examples where f"(x)=0 doesn't mean Point of Inflexion).
Using the Second Derivative (5 of 5: Where the concavity changes but f"(x) doesn't exist).
Points of Inflexion: Step-by-Step Guide.
Stationary Points: Step-by-Step Guide.
Graphing Derivatives (1 of 4: Graphing the Derivative functions from the original function).
Graphing Derivatives (2 of 4: Using the Derivative function to determine the original function).
Graphing Derivatives (3 of 4: Process to graphically find the primitive).
Graphing Derivatives (4 of 4: Harder Derivatives [Discontinuous Functions]).
Curve Sketching with Calculus (1 of 3: Using Calculus to find the Stationary Points).
Curve Sketching with Calculus (2 of 3: Finding Intercepts and Regions to assist Curve Sketching).
Curve Sketching with Calculus (3 of 3: Using the Stationary Points to assist with Curve Sketching).
Max/Min Problems (1 of 3: Introduction to Optimisation).
Max/Min Problems (2 of 3: Using a Table of Values to Determine Absolute Maxs/Mins).
Max/Min Problems (3 of 3: Finding the Maximum point of more complex equations).
Optimisation (1 of 3: Setting up equations to "optimise" for max volume).
Max/Min Distance Problems (1 of 4: Introducing a Parameter to solve Max/Min Problems).
Max/Min Distance Problems (2 of 4: Discussing Restrictions on Max/Min Distance Problems ).
Optimisation (2 of 3: Using the Derivative to find possible turning points).
Optimisation (3 of 3: Finding the Hidden Conditions and Solving the Problem).
Max/Min Distance Problems (3 of 4: A Plausible real world problem).
Max/Min Distance Problems (4 of 4: Why is it not essential to test nature of T.P. in this scenario).
Equations of Tangents & Normals.
Understanding Stationary Points (1 of 3: Classifications).
Understanding Stationary Points (2 of 3: Location).
Understanding Stationary Points (3 of 3: Determining nature).
Critical Values (1 of 2: Piecemeal functions).
Critical Values (2 of 2: Cusps).
Graphing Stationary Points (1 of 3: Using the first derivative).
Graphing Stationary Points (2 of 3: Notation of the second derivative).
Graphing Stationary Points (3 of 3: Visualising the second derivative).
Using the Second Derivative (1 of 2: Locating stationary points).
Using the Second Derivative (2 of 2: Determining nature of stationary points).
Flowchart for Testing Stationary Points.
Points of Inflexion (1 of 2: Understanding & identifying).
Points of Inflexion (2 of 2: Discontinuities in the second derivative).
Mathematics Ext 1 Exam Questions (4 of 4: Stationary points).
Absolute Maximum/Minimum (1 of 2: Domain restricted polynomial).
Absolute Maximum/Minimum (2 of 2: Unusual rational function).
Applications of Maximisation/Minimisation (1 of 2: Largest rectangle area question).
Applications of Maximisation/Minimisation (2 of 2: Interpreting the calculus).
Max/Min in Geometry (1 of 3: General principles).
Max/Min in Geometry (2 of 3: Cylinder in a cone).
Max/Min in Geometry (3 of 3: Applying calculus).
Interpreting a Graph w/ Calculus (1 of 2: Sketching the curve).
Using Derivatives of Trigonometric Functions (2 of 2: Sketching a curve).
Tricky Max/Min Question: Finding the Derivative.
Tricky Max/Min Question: Solving for Stationary Points.
Using Calculus to Graph y = x – e^x.
Graphing Log Function with Calculus (1 of 3: Finding Domain and Derivative).
Graphing Log Function with Calculus (2 of 3: Understanding the Derivative).
Graphing Log Function with Calculus (3 of 3: Sketching the Curve).
Sign of the Derivative (7 of 7: Determining nature of stationary points).
Sign of the Derivative (6 of 7: Locating stationary points).
Sign of the Derivative (5 of 7: Distinguishing stationary points).
Sign of the Derivative (4 of 7: Vertical tangent).
Sign of the Derivative (3 of 7: Basic worked example).
Sign of the Derivative (2 of 7: Increasing, stationary, decreasing).
Sign of the Derivative (1 of 7: Differentiation review questions).
Classifying Stationary Points (1 of 3: Review of point types).
Classifying Stationary Points (2 of 3: Flowchart for locating points).
Classifying Stationary Points (3 of 3: Flowchart for determining nature).
Determine Function from Stationary Points.
The Second Derivative (1 of 3: Investigating a pandemic curve).
The Second Derivative (2 of 3: Exploring first derivative values).
The Second Derivative (3 of 3: Notation).
Geometry of the Derivatives (1 of 6: Review question).
Geometry of the Derivatives (2 of 6: Exploring gradient & concavity).
Geometry of the Derivatives (3 of 6: Points of inflexion).
Geometry of the Derivatives (4 of 6: Determining max/min with second derivative).
Geometry of the Derivatives (5 of 6: What if the second derivative equals 0?).
Geometry of the Derivatives (6 of 6: How do I choose which derivative to use?).
Identifying Important Points with Calculus (worked solution).
What is Optimisation? (1 of 6: Review questions).
What is Optimisation? (2 of 6: The barbecue scenario).
What is Optimisation? (3 of 6: Example derivative).
What is Optimisation? (4 of 6: Checking endpoints).
What is Optimisation? (5 of 6: Constructing a model).
What is Optimisation? (6 of 6: Finding the minimum).
Derivatives of Motion (1 of 3: What does each derivative signify?).
Derivatives of Motion (3 of 3: Understanding movement).
Derivatives of Motion (2 of 3: Graphs for displacement, velocity & acceleration).
Interpreting Motion Graphically (1 of 4: Direction of movement).
Interpreting Motion Graphically (2 of 4: Identifying specific features).
Interpreting Motion Graphically (3 of 4: Exploring acceleration).
Interpreting Motion Graphically (4 of 4: Velocity & acceleration graphs).