Optimization in several variables and Lagrange multipliers

By the end you’ll be able to

• Find critical points of $f(x, y)$ and classify them as local maxima, minima or saddle points with the Hessian (second-derivative) test
• Find absolute extrema on closed, bounded regions by checking interior critical points and every piece of the boundary
• Apply Lagrange multipliers to optimize a function subject to one constraint, and set up problems with two constraints