IB Maths AA HL Sl 5 8 Extrema Optimization and Inflexion Questions

Practise IB Mathematics HL 5.8 by applying extrema, optimization and inflexion methods to questions from the Question Bank.

Exam points

Find local maxima and minima using first-derivative sign changes or second-derivative tests, and identify inflexion points and concavity from derivative information.
Form and solve optimization models for profit, area or volume, stating the feasible domain and interpreting the stationary solution in context.

[Maximum number: 2]

The following question explores features of a family of curves. The family is then linked to a homogeneous differential equation.
Consider the curve given by $y=\frac{x\left(x^{2}-16\right)}{x^{2}+16}$ .

State the coordinates of the local maximum point and the coordinates of the local minimum point.

Max $(-1.94,1.20)(-1.94347 \ldots, 1.20113 \ldots)$

Min $(1.94,-1.20)(1.94347 \ldots,-1.20113 \ldots)$

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IB Maths AA HL Sl 5 8 Extrema Optimization and Inflexion Questions question 1