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IB Maths AI SL 5.1 Limits & derivative concept

IB Maths AI SL 5.1 Limits & derivative concept
IB Mathematics: applications and interpretation guide, first assessment 2021

Students practise calculating derivatives from first principles or power rules, then interpreting dy/dx as a rate of change in context—e.g., cm per day or m/s.

How this is tested

  • calculate dy/dx at a given t-value, then interpret the number as a rate with units and time reference
  • substitute x = 2 into a given derivative expression to find gradient of a curve or model at that point
  • use the derivative sign at a given time to state increase or decrease

Question 4(c)(i)

Jenny designs a flexible suspension bridge, spanning 10 metres over the Swinburne Creek.
Jenny believes that when no people are on the bridge, the height, y, of the walkway on the bridge above the creek can be modelled by

y=ax2+bx+c for 0≤x≤10.y=a x^{2}+b x+c \text { for } 0 \leq x \leq 10 .

She uses a coordinate system where the origin is directly below one side of the bridge, as shown in the following diagram. All distances are measured in metres.

According to this model, the points P(0,4), Q(2,3.936) and R(5,3.9) will be located on the walkway of the bridge. Point R is the lowest point of the bridge.

Figure for Question 4(c)(i) — IB Maths AI SL

For Jenny's model find

dy dx\frac{\mathrm{d} y}{\mathrm{~d} x};