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IB Maths AI SL 5.6 Stationary points Question Bank

Practise IB Mathematics SL/HL 5.6 by applying stationary points methods to exam-style questions.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation SL
Level
SL

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

SL 5.6—Stationary points question 1

[Maximum number: 4]

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

f(x)=0.001x3−0.12x2+4.05x+3, for 0≤x≤60f(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 SL 5.6—Stationary points question 1 — IB Maths AI SL

Point O has coordinates (0,0).

Find the coordinates of M .

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