Applications of Differentiation
The second derivative, concavity, inflection points, curve sketching, optimisation problems, and kinematics.
Active lessons
11
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
Diagnostic
Take the topic test
A timed, ~60-minute test drawn at random across all 6 subtopics of this unit. You get a marked result, a predicted band, and a clear list of which subtopics to re-practise.
Unit pathway
Lesson pathway
10 of 10 active
Lesson 1
Second Derivative Test
Use the second derivative to classify stationary points as local maxima or local minima.
Lesson 2
Curve Sketching with Derivatives
Combine intercepts, stationary points, derivative signs, and concavity to sketch polynomial curves.
Lesson 3
Optimisation Problems
Form objective functions and use derivatives to solve maximum and minimum problems.
Lesson 4
Rates of Change Applications
Interpret derivatives as instantaneous rates of change in applied contexts.
Lesson 5
Mixed Differential Calculus Exam Practice
Practise mixed HSC-style differential calculus questions that combine skills, reasoning, and interpretation.
Lesson 6
Second Derivative, Concavity and Points of Inflection
Use the second derivative to determine concavity and test possible points of inflection.
Lesson 7
Stationary Point Classification
Classify stationary points using the second derivative test and first derivative sign test.
Lesson 8
Curve Sketching with Calculus
Combine intercepts, stationary points, concavity and end behaviour to interpret curve sketches without drawing.
Lesson 9
Kinematics and Rates of Change
Use derivatives for displacement, velocity, acceleration and motion interpretation.
Lesson 10
Applications of Differentiation Exam Practice
Practise mixed HSC-style applications involving concavity, stationary points, curve sketching, optimisation and motion.