Edexcel IGCSE Maths 复习笔记 3.11.3 Differentiation - Problem Solving

What problems could involve differentiation?

• Differentiation allows analysis of how one quantity changes as another does
• The 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 (ie. speed – see Kinematics)

   

• 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
  • eg the maximum volume of a box made from a flat sheet of material
  • eg 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

   

• A third type of problem involving the motion of an object is dealt under the separate set of notes Kinematics