Chapter 15, Problem 10P

Given the following function,

$f\left(x,y\right)=8x+x^2+12y+4y^2-2xy$

use a software package to determine the minimum:

(a) Graphically.

(b) Numerically.

(c) Substitute the result of (b) back into the function to determine the minimum $f\left(x,y\right)$.

(d) Determine the Hessian and its determinant, and substitute the result of part (b) back into the latter to verify that a minimum has been detected.