Problem Solving with Differentiation | Mathematics for GCSE/IGCSE - Year 11 PDF Download

What problems could involve differentiation?

• Differentiation allows us to analyze how one quantity changes concerning another.
• The derived function, also known as the gradient function or derivative, provides a measure of the rate of change.
• Various problems involving a variable quantity can be addressed through differentiation. For instance:
  • 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, indicating its speed.
• Additionally, differentiation can be applied to problems based on the graph of a curve, such as determining:
  • The distance between two turning points on the curve.
  • The area of a shape formed by points on the curve, like turning points and axis 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 hold significance in the context of the problem:
  • For instance, the maximum volume of a box formed from a flat sheet of material or the minimum height of water in a reservoir.
• These scenarios are often referred to as optimization problems.
• The maximum or minimum value represents the optimal or best solution to the problem.