Differential calculus: cubic and quartic functions

• Students apply the concept of a limit in the context of the rate of change of a non-linear function.
• Students interpret the gradient of the tangent to a curve as being the rate of change of the function.
• Students apply first principles methods to differentiate the functions: s(t) = t³ – 2 and s(t) = t⁴ + t².
• Students interpret the concept of a derivative of a function. They identify that for s(t) = t³ – 2 the derivative is f'(t) = 3t², and that for s(t) = t⁴ + t² the derivative is f'(t) = 4t³ + 2t.

• Introduces students to the language, notation and methods of differential calculus.
• Provides opportunities for students to engage in first principles differentiation of a basic polynomial function.
• Tabulates results to help students find patterns in the gradients at different points on the curve.
• Summarises key statements related to derivatives and average and instantaneous velocities.
• Displays feedback for correct and incorrect answers.

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