Absolute Max|Min of Multivariable Function

Visualizing these with GeoGebra 3D:

In this video we talk about how to find the absolute extrema (max/min) of a multivariable function over a specified region in the plane. Specifically we're going to find the absolute maximum and minimum values of the function f(x,y) = x^2 + y^2 - 2x -4y on the region where x is positive, y is between 0 and 3, and y is greater than or equal to x. We follow a definite plan: sketch the region and note the corners (vertices), find the critical points within the region, find the traces along the edges and see what happens there, and then make a table to compare values of the function.

This is definitely something you'll see in any Calculus III or Multivariable Calculus course!

calc iii,calculus iii,multivariable,absolute extrema,absolut maximum,absolute minimum,absolute max/min,critical points,critical point,trace,parameterize,candidates test,candidate test,optimization,constraints,