Use lagrange multipliers to find the points on the cone z2 = x2 + y2 that are closest to (16, 6, 0).

Minimize subject to . The Lagrangian would be



and has partial derivatives



Setting each partial derivative to 0, we have



From the third equation, it follows that either or . In the second case, we arrive at a contradiction:



since both and must be non-negative, yet this would mean e.g. . So it must be that .

The first and second equations then tell us that




from which we obtain .

Thus the points on the cone closest to (16, 6, 0) are .

C.1because in the function table shown when you plug -2 in for x your outcome is 1.

Ithink you're supposed to multiply 12.50 which is how much he makes per hour and then multiply it by each number then add whats left togrther and there's your answer