SOLUTION: Construct a rational function that will help solve the problem. Then, use a calculator to answer the question. An open box with a square base is to have a volume of 32 cubic in

Question 1128295: Construct a rational function that will help solve the problem. Then, use a calculator to answer the question.
An open box with a square base is to have a volume of 32 cubic inches. Find the dimensions of the box that will have minimum surface area. Let x = length of the side of the base.
My work is: A=4xh +x^2
32=x^2h
32/x^2 = x^2h/ x^2
32/x^2 = h
A(x)= 4(32/ x^2) + x^2
A(x)= 128/x + x^2

When I went to grab it, the minimum surface area looked like it was at -5.07
So with that I did the following: h= 128/5^2
H= 128/25 which resulted in 5.12. However, those answers proved to be incorrect.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
It is good to figure out by ourselves if we have the correct solution.
First, think if the answer seems possible.
You should not get a negative value for ,
because it is the length of the side of a box,
so is obviously a wrong result.
Maybe you could have found , but not .

From and
you do get

, not

How do we check if a formula like that is right?
If for each you calculate ,
and then use the two formulas,
A=4xh +x^2 and A(x)= 128/x + x^2
do you get the same results?
I did:

If I were to graph A(x),
I would see that the minimum is at with .
I suppose you are expected to interpret "use a calculator to answer the question"
to mean use a certain graphing calculator to graph A(x).
You might have to use your expensive graphing calculator for the SAT.
I guess that is why they teach you to use it.
I have never been asked to use a graphing calculator at work,
but most of us spend a lot of time in front of computers with Microsoft Excel on them,
and we use it a lot for graphing.
It would be nice if schools taught you to use Excel.

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