About this topic
Before you begin
Use partial derivatives, gradients, tangent planes and stationary points of surfaces.
Learning goals
- Calculate and interpret first- and second-order partial derivatives
- Find and classify maxima, minima and saddle points of a function of two variables
- Find tangent and normal planes and local linear and quadratic approximations
- Use the gradient vector and directional derivatives
Syllabus statements covered
- Include: functions of two variables and surfaces z = f(x, y); first order and second order partial derivatives; minimum, maximum and saddle points; normal and tangent planes and local linearisation; directional derivatives and gradient; quadratic approximations; local maximum and minimum problems. Exclude Jacobian matrix, Lagrange multipliers and constrained optimisation.
In this topic
Partial derivatives and stationary points
Differentiate surfaces partially, use gradients, tangent planes and linear estimates, and classify maxima, minima and saddle points.