Applications of Differentiation
Use derivatives to understand shape and behaviour.
Calculus
Stationary Points
Local maxima, local minima and horizontal inflection.
CalculusSecond Derivative Test
Classify stationary points using concavity.
CalculusPoints of Inflection
Concavity changes and horizontal inflection.
CalculusTangents and Normals
Equations of tangent and normal lines.
CalculusTangents and Normals: Equations
Derivative gradients and point-gradient form.
CalculusOptimisation
Model maximum/minimum problems.
Useful checklist
- Differentiate.
- Solve the relevant derivative equation.
- Substitute back into the original function to get coordinates.
- Use sign changes or the second derivative to interpret the point.
- Write the final answer in context.