[填空题]
Jack makes an open contain4 nsqk(k wbm*1er in the shape of a cuboid with square base, avl c kz:3xwv/;vn;fvev3z*y ( s shown lfzvev(: ;33v vn kv*yz;cw/xin the following diagram.
The container has base length $x \mathrm{~m}$ and height $y \mathrm{~m}$ . The volume is $32 \mathrm{~m}^{3}$ .
Let A(x) be the outside surface area of the container.
1. Show that $A(x)=\frac{128}{x}+x^{2}$.
2. Find $A^{\prime}(x)$ .
3. Given that the outside surface area is a minimum, find the base length of the container.
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.
