CAIE IGCSE Mathematics Maxima and Minima

Review CAIE IGCSE Mathematics maxima and minima decisions through second derivatives, sketches and gradients on either side of turning points.

Exam points

use the second derivative at a turning point to justify maximum or minimum
compare gradients or y-values on either side of a turning point to support the decision
interpret a sketch of a positive or negative cubic to classify its turning points

[Maximum number: 3]

A curve has the equation $y=x^{3}+8 x^{2}+5 x$ .

Determine whether each of the turning points is a maximum or a minimum. Give reasons for your answers.

$\left(-\frac{1}{3},-\frac{22}{27}\right)$ minimum
(-5,50) maximum with correct reasons
B2 for one correct with reason, or M1 for correct attempt such as second derivatives, gradients, or sketching.

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E2.12.4 Distinguish maxima and minima question 1