1. Let z = f(x, y) = 3x2 + 4y2 - xy - 2. Use the Lagrange multipliers to find the values of x and y that will give the relative extrema of z = f(x, y), subject to 2x + v = 21. Find the extreme value of f 2. Using the Lagrange multipliers find the values of x and y to find the relative maximum of z = f(x, y) = x2 - 10y2, subject to x - y = 18. 4. Using the Lagrange multipliers find the values of x, y and z to find the relative maximum of w = f (x, y, z) = xyz', subject to x + y + z =6