Solve the following and show the complete solution. 1. Find Duf at P: f(x,y) = sin(8x 5y) ; P (5 ,8)): u = (gt31') (10 pts) 2. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of their squares is as small as possible. Give the sum of the squares. (10 pts) 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x y + z = 2 and x + y 82 = 4. (10pts)