IB Maths AA HL 5.8 Extrema, optimization and inflexion Question Bank

Practise IB Mathematics SL/HL 5.8 by applying extrema, optimization and inflexion methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[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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SL 5.8—Extrema, optimization and inflexion question 1