Find the maximum and minimum values of the function f(x,y) = x2 ‐2y subject to the constraint
that x2 + y2 = 9 and please show calculations
We should use Lagrange multipliers and Extreme value theorem. Let's construct the system of equations: 2x = 2λ x; -2 = 2λ y; x2 + y2 = 9. Hence: λ = 1, y = -1, x2 = 8. The function has one extreme value: f(x,y) = 8 + 2 = 10. f(√5, 2) = 5 - 2 = 3. Thus f(x,y) = 10 is the maximum of the given function subject to constraint that x2 + y2 = 9.