Applications of Differentiation

Delve into the world of calculus with this comprehensive 20-hour course on applications of differentiation. Master concepts like finding stationary points, understanding motion, and solving optimization problems. Explore the geometrical applications of calculus, learn to sketch curves using derivatives, and tackle max/min problems in various contexts. Gain proficiency in interpreting graphs, analyzing motion, and applying the second derivative. Through a series of lectures and problem-solving exercises, develop a deep understanding of critical calculus concepts and their real-world applications.

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).