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IB DP Maths: AI SL复习笔记5.1.3 Modelling with Differentiation

Category: IB课程, 教材笔记, 福利干货 Date: 2022年7月19日下午5:04

Recall that differentiation is about the rate of change of a function and provides a way of finding minimum and maximum values of a function
Anything that involves maximising or minimising a quantity can be modelled using differentiation; for example
- minimising the cost of raw materials in manufacturing a product
- the maximum height a football could reach when kicked
These are called optimisation problems

The quantity being optimised needs to be dependent on a single variable
- If other variables are initially involved, constraints or assumptions about them will need to be made; for example
  - minimising the cost of the main raw material – timber in manufacturing furniture say – the cost of screws, glue, varnish, etc can be fixed or considered negligible
- Other modelling assumptions may have to be made too; for example
  - ignoring air resistance and wind when modelling the path of a kicked football

STEP 1

Rewrite the quantity to be optimised as a single variable, using any constraints given in the question

STEP 2

Use your GDC to find the (local) maximum or minimum points as required

Plot the graph of the function and use the graphing features of the GDC to “solve for minimum/maximum” as required

STEP 3

Note down the solution from your GDC and interpret the answer(s) in the context of the question

The first part of rewriting a quantity as a single variable is often a “show that” question – this means you may still be able to access later parts of the question even if you can’t do this bit