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