Problem Solving with Differentiation (CIE IGCSE Maths: Extended)

What problems could involve differentiation?

• Differentiation allows analysis of how one quantity changes as another does
• The derived function (gradient function / derivative) gives a measure of the rate of change
• Problems involving a variable quantity can involve differentiation
  • How the area of a rectangle changes as its length varies
  • How the volume of a cylinder changes as its radius varies
  • How the position of a car changes over time (i.e. its speed)

• Problems based on the graph of a curve may also arise
  • The distance between two turning points
  • The area of a shape formed by points on the curve such as turning points and axes intercepts

How do I solve problems involving differentiation?

• Problems generally fall into two categories:

1. Graph-based problems

• These problems are based around the graph of a curve and its turning points

2. Maximum/Minimum problems

• • The maximum or minimum values have a meaning in the question
    e.g. the maximum volume of a box made from a flat sheet of material

    e.g. the minimum height of water in a reservoir

  • These are sometimes called optimisation problems

    The maximum or minimum value gives the optimal (ideal/best) solution to the problem