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Learners interpret average gradient and the derivative, calculate the first derivative from first principles, apply the basic rules for algebraic functions, and use the second derivative to identify concavity, extreme points and points of inflection.
Learners factorise cubic functions, find roots, and locate stationary points and points of inflection; follow a step-by-step calculus procedure to sketch different cubic types; and interpret intercepts, turning points, concavity and related inequalities.
Learners revise the first- and second-derivative tests to classify extrema, then model a problem situation as a function of one variable and optimise it. They apply this method to area and volume, rates of change, engineering design, and profit or cost.
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