Course: Year 12 Mathematics Advanced

Applications of Differentiation

A HSC-focused unit for second derivative applications, curve sketching, optimisation, motion and rate interpretation.

Active lessons

6

Planned lessons

6

Lesson sequence

Learn -> Guided Practice -> Independent Practice -> Mastery Quiz

How to use this unit

  • Review derivative techniques before starting optimisation or kinematics.
  • Use the concavity lessons before curve-sketch interpretation.
  • For optimisation, check whether the question asks for the input or the optimal value.
  • For motion, keep displacement, velocity, acceleration, speed and distance separate.

What this unit covers

Second derivative and concavity
Points of inflection
Stationary point classification
Curve sketching with calculus
Optimisation
Kinematics and rates of change

Unit pathway

Lesson pathway

6 of 6 active

1

Lesson 1

Second Derivative, Concavity and Points of Inflection

Use the second derivative to determine concavity and test possible points of inflection.

Active
2

Lesson 2

Stationary Point Classification

Classify stationary points using the second derivative test and first derivative sign test.

Active
3

Lesson 3

Curve Sketching with Calculus

Combine intercepts, stationary points, concavity and end behaviour to interpret curve sketches without drawing.

Active
4

Lesson 4

Optimisation

Use differentiation to solve practical maximum and minimum problems with domain restrictions.

Active
5

Lesson 5

Kinematics and Rates of Change

Use derivatives for displacement, velocity, acceleration and motion interpretation.

Active
6