IB Maths AI HL 5.6 Stationary points Question Bank

Practise IB Mathematics SL/HL 5.6 by applying stationary points 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: 5]

Linda owns a field, represented by the shaded region R. The plan view of the field is shown in the following diagram, where both axes represent distance and are measured in metres.

Figure for Question SL 5.6—Stationary points question 1 — IB Maths AI HL

The segments [AB], [CD] and [AD] respectively represent the western, eastern and southern boundaries of the field. The function, f(x), models the northern boundary of the field between points B and C and is given by

f(x)=\frac{-x^{2}}{50}+2 x+30, \text { for } 0 \leq x \leq 70

Hence find the coordinates of the point on the field that is furthest north.

Point A has coordinates (0,0), point B has coordinates (0,30), point C has coordinates (70,72) and point D has coordinates (70,0).

$0=\frac{-x}{25}+2$ OR sketch of $f^{\prime}(x)$ with x-intercept indicated M1
$x=50 \quad$ A1
$y=80 \quad$ A1
(50,80)
Note: Award M0A0A1 for the coordinate (50,80) seen either with no working or found from a graph of f(x).

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SL 5.6—Stationary points question 1