[填空题]
Jack makes an open container in the shape of a cubf xo:arlyr,s;a:po 3/)+ gmt eoid with square bap:qa:k 8u s(xixia: r0se, as shown in the following diagx:(puki8:sir0ax a:q ram.
The container has base length x m and height y m. The volume is 32 $m^3$.
Let A(x) be the outside surface area of the container.
1. Show that A(x)=$\frac{128}{x}+x^{2}$ .
2. Find $A^{\prime}(x)$=ax-$\frac{128}{x^2}$,a= .
3. Given that the outside surface area is a minimum, find the base length of the container. x= m.
4. Jack coats the outside of the container with waterproof resin. A can of resin covers a surface area of 5$ \mathrm{~m}^{2}$ and costs $\$$ 15 . Find the total cost of the cans needed to coat the container.
