A LevelMaths: Pure 1CIERevision Notes5. Differentiation5.2 Applications of Differentiation5.2.6 Modelling with Differentiation inc. Optimisation

Modelling with Differentiation inc. Optimisation (CIE A Level Maths: Pure 1)

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Modelling with Differentiation inc. Optimisation

How can I use differentiation to solve modelling questions?

  • Derivatives can be calculated for any variables – not just y and x
  • In every case the derivative is a formula giving the rate of change of one variable with respect to the other variable

 Model Diff Illustr 1, A Level & AS Maths: Pure revision notes

 

  • Differentiation can be used to find maximum and minimum points of a function (see Stationary Points)
  • Therefore it can be used to solve maximisation and minimisation problems in modelling questions

Model Diff Illustr 2, A Level & AS Maths: Pure revision notes

Examiner Tip

Exam questions on this topic will often be divided into two parts:

  • First a 'Show that...' part where you derive a given formula from the information in the question
  • And then a 'Find...' part where you use differentiation to answer a question about the formula

Even if you can't answer the first part you can still use the formula to answer the second part.

Worked example

Model Diff Example_A, A Level & AS Level Pure Maths Revision Notes

Model Diff Example_BC, A Level & AS Maths: Pure revision notes

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    Roger

    Author: Roger

    Expertise: Maths

    Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.