Find the critical points of <em>f(x, y) </em>:
Subtract the first equation from the second to eliminate <em>x</em> and solve for <em>y</em> :
Solve for <em>x</em> :
So <em>f(x, y)</em> has one critical point at (0, 2).
Compute the Hessian determinant of <em>f(x, y)</em> at this point:
The Hessian has determinant 24 > 0, which indicates a minimum, so the minimum value of <em>f(x, y)</em> is <em>f(</em>0, 2<em>)</em> = 6.