Determining the maximum and minimum values of function

Question

Determine the maximum and minimum values of the function f(x,y)=x^2+y^2-2x-4y+5 in the set D = {( x ,y )∈R^2 / x^2 + y^2 ≤ 45}.

Answer 1

Find local max and mins inside D using first and second partial derivatives.

Find max and mins on the boundary of D (a circle of radius root(45)) using Lagrange multipliers.

The absolute max is the largest of all found points and the absolute min is the smallest of all found points.