Needing to know how to minimize cost of box

[lbaird]

A rectangular container with a square base and a volume of 128 ft^3. The cost of the materials for the top and four sides is $2 per ft ^2. The cost of the materials for the bottom is $6 per ft^2. Find the dimensions of the box that minimizes the cost of the materials, and find the minimum cost.

So far, I have x^2(h)=128
h=128/x^2

Cost = 6x^2+10(128/x^2)

Is this the way to begin? Don't I need to take the derivative of something in order to minimize.

Thanks

 

[skeeter]

x²h = 128
h = 128/x²

cost for the bottom ... 6x²
cost for the top ... 2x²
cost for 4 sides ... 2(4xh) = 8xh = 8x(128/x²) = 1024/x

total cost ...

C = 8x² + 1024/x

now find dC/dx and minimize