Mathematics I (Calculus) - Old Questions

19. Find the absolute maximum and minimum values of f(x,y) = 2 + 2x + 2y – x²– y² on the triangular plate in the first quadrant bounded by lines x = 0, y = 0 and x + y =9.

OR

Find the points on the curve xy²= 54 nearest to the origin. How are the Lagrange multipliers defined?