Solve the Volume of an Open Box with a Square Base | Neat Function Problem

[Gay4Functions]

Homework Statement

An open box wit ha square base is required to have a volume of 38 cubic feet. Express the amount A of material that is needed to make such a box as a function of the length x of a side of the square base. We need to find the solution for the least amount of material used.

Homework Equations

The Attempt at a Solution

 

[symbolipoint]

Initially, your question description seems incomplete. Do you have a preformed net which merely needs to be folded into the box form? You made no comment related to the height of this box with the square base of x by x. Better----> an expression for height can be made. h*x*x=38. h is the height. If A is area of the net, then an expression can be made for this area from the numbers of h and x.

note: I tried to make a 'strike-through' of the first sentence but the tagging seems to not work.

 

[symbolipoint]

After trying that exercise myself, the original question belongs better in the Calculus board. The solution process yields a rational expression; you want to minimize the Area function.

On the other hand, if you would use a graphing program, you can determine a good value fairly easily without the use of Calculus.