The function f(x, y) = xy has an absolute maximum value and absolute minimum value subject to the constraint 2x^2 + 3y^2 - 3xy = 49. Use Lagrange multipliers to find these values. A. Find the gradient of f(x, y) = 3xy.
B. Find the gradient of g(x, y) = x2 + y2 - xy-9.
C. Write the Lagrange multiplier conditions.
A. 3xy = M2x - y), 3xy = M2y - x), x2 + y2 - xy - 9 = 0
B. 3x = M(2x - y), 3y = M2y - x), 3xy = 0
C. 3y = M(2x - y), 3x = M(2y – x), x² + y2 - xy - 9 = 0
D. 3x = M(2x - y), 3y = M2y - x), x2 + y2 - xy - 9 = 0
The absolute maximum value is:.
The absolute minimum value is:.