CAIE IGCSE Mathematics Extended E2.12.4 Distinguish Maxima and Minima Questions

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, gradients or y-values on either side, and curve sketches to classify turning points as maxima or minima.

[Maximum number: 3]

A curve has equation $y=4 x^{3}-3 x+3$ .

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

$\begin{aligned} \left(-\frac{1}{2},4\right)&\text{ maximum with reason}\\ \left(\frac{1}{2},2\right)&\text{ minimum with reason} \end{aligned}$
B2 for one correct with reason, or M1 for a correct attempt such as second derivative, gradients, or sketch.

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CAIE IGCSE Mathematics Extended E2.12.4 Distinguish Maxima and Minima Questions question 1