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5 . Use the method of Lagrange Multipliers to find the minimum value of f (x, y, z) =x2+2y2+4z2 subject to the constraint xyz =16V2. Show all work. 5 pts 6. Find the coordinates of the point on the ellipse x2 + 6y2 + 3xy =90 with the greatest x coordinate. 4 pts2. Find all critical points and local maximums, minimums, and saddle points of the following functions. Show all work. A) f (x, y ) = 1x4-x3 + 6xy+ 12 Critical Points 4 pts B) f (x, y ) = x2y+ 23+x2+5x2 Critical Points 4 ptsFind the absolute maximum and minimum values of the function f(x, y) =x2+ y on the region R bounded by the graphs of y = x2 and y = x+ 2. Sketch the domain region and show all critical values and work.3. Rectangular boxes with a volume of 8 ft' are to be made of three materials. The material for the bottom of the box costs $12 per ft?, the top of the box costs $4 per ft2 and the material for the sides costs $10 per ft2. What are the dimensions of the box that minimizes the cost of the box? Show all work. Round final dimensions of the box to the nearest tenth of a foot. (1 decimal place) 4 pts 4. Use the method of Lagrange Multipliers to find the maximum and minimum values of f(x, y) =xy2 subject to the constraint x2 + y =8. Show all work. 4 pts