Find the absolute maximum and minimum values of f on the set
d. f(x, y) = 4x + 6y ? x2 ? y2 + 5, d = {(x, y) | 0 ? x ? 4, 0 ? y ? 5}

We are asked to determine the minima or the maxima of the given functions. The minima or maxima of the expressions can be determined by taking the first derivative of the equation and then equating the derived equation to zero. we next find the values of x. The minima coordinates can be determined by subsittuting x back to the original equation to find y. in this case, 
 
1) x2 = 4x + 6y
2x = 4 + 6 y' 
y' = x/3 + 2/3 = 0
x = -2
y = -2/3

2) y2 + 5 = 4x + 6y
2y y '  = 4 +6y'
y' = 0
y' (2y -6) = 4

Yes, two vertical lines can be complementary