IB Maths AI SL 5.6 Stationary Points Questions

Practise solving f′(x) = 0 for stationary points, classifying local extrema and distinguishing them from absolute extrema on a stated domain.

Exam points

Solve f′(x)=0 to find stationary-point x-values, using technology where appropriate.
Classify local maxima and minima from derivative behaviour or the graph.
Distinguish local from absolute extrema on a stated domain and interpret the result.

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Zheng models the height of a section of a rollercoaster.
She uses the function

f(x)=0.001 x^{3}-0.12 x^{2}+4.05 x+3, \text { for } 0 \leq x \leq 60

where x is the horizontal distance from the left-hand end of the section and f(x) is the vertical height. Distances are measured in metres.

Zheng's model is shown on the following graph of y=f(x).

Figure for Question IB Maths AI SL 5.6 Stationary Points Questions question 1 — IB Maths AI SL

Point O has coordinates (0,0).

Find the coordinates of M .

$x=24.2(24.1886 \ldots), y=44.9(44.9056 \ldots)$ or (24.2,44.9)

Note: Award A1A0 if parentheses are omitted.

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IB Maths AI SL 5.6 Stationary Points Questions question 1