Use Lagrange multipliers to find the minimum and maximum of the given function f(x,y) subject to to the constraint g(x,y)=c f(x,y) = 4xy subject to x² + y² = 8.

Use Lagrange multipliers to find the maximum and minimum values of f (x, y) = xy subject to the constraint 9x +y = 18 if such values exist.

Find the minimum and maximum values of the function f(x, y) = x²y4 subject to the constraint x² - y² + z = 0.

Use Lagrange multipliers to find the maximum and minimum values of f(x, y, z) = xy²z³ (if they exist) subject to x2 + y2 + 2z² = 100.