Lecture 10 Optimization problems for multivariable functions

Up to now, we have encountered three types of critical points for functions f(x,y) of two variables: 1. Local minima: The point (0,0) is a local minimum for the function f(x,y) = x2 + y2, the graph of which is sketched below. O x y z z = x2 +y2 A plot of the countours/level sets of this function will also help us to understand the behaviour