7 Differentiation
7.1 Limits
7.1.1 Evaluating limits
7.1.2 Properties of limits
7.1.3 When a limit does not exist
7.1.4 Limits at infinity
7.2 Continuity
7.3 The derivative
7.3.1 Differentiation from first principles
7.4 Rules for differentiation
7.5 Implicit differentiation
7.6 The second derivative
7.7 Applications
7.7.1 Gradient of a curve
7.7.2 Increasing and decreasing functions
7.7.3 Turning points
7.7.4 Points of inflexion
7.7.5 Greatest and least values on an interval
7.7.6 Optimisation
7.8 Practice problems
7.1.1 Evaluating limits
7.1.2 Properties of limits
7.1.3 When a limit does not exist
7.1.4 Limits at infinity
7.2 Continuity
7.3 The derivative
7.3.1 Differentiation from first principles
7.4 Rules for differentiation
7.5 Implicit differentiation
7.6 The second derivative
7.7 Applications
7.7.1 Gradient of a curve
7.7.2 Increasing and decreasing functions
7.7.3 Turning points
7.7.4 Points of inflexion
7.7.5 Greatest and least values on an interval
7.7.6 Optimisation
7.8 Practice problems
Questions on this section
Stuck on something here? Ask below and it stays attached to this topic.