1. A sheet of cardboard 3 ft by 4 ft (use meters if that helps since it's just a label) will be made into a box by cutting equal sized squares from each corner and folding up the four edges. What will be the dimensions of the box with largest volume?
2. Consider all triangles formed by the lines passing through the point (8/9,3) and both the x and y axes. Find the dimensions of the triangle with the shortes hypotenuse.
3. Find the point (x,y) on the graph of y = sqrt(x) nearest the point (4,0)
4. A cylindrical can is to hold 20pi m^3. The material ofr the top and bottom costs $10/m^2 and material for the side costs $8/m^2. Find the radius r and height h of the most economical can.
These are extra credit for my calculus class (I don't really need it since I have 95% in it already and just got a 100% on my final, but it's still nice to have and i'm curious how to do the problems.)
