[填空题]
Jack makes an open container in the shape of a cuboid with squa - *bxkfijn3j7re baseog87o0ie pdb(w7 ffhw(cn3g,jl+s s+, as shown in the following diagram80,gphj(nsc efo7 osbw dw +(7ifg l+3.
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.
