Jamal wants to make a box with no top out of a $24$ $inch^2$ piece of cardboard. She plans to cut smaller squares of equal size from the corners of the cardboard and fold up the resulting sides. By rounding to the nearest inch, what size of the square cut outs will create a box with the largest volume? I was thinking of using calculator, but I don't think that will work How do I solve this?
So the things i got are that the length
L=24-x or is 24-2x? To find a volume you do lwh But i dont think i did it right
Sorry for not editing the post nicely im doing this in my phone
Imagine cutting out the four little squares and folding the four flaps upward. Then we create a box whose bottom is a $24-2x$ by $24-2x$ square.
The volume of the box is then $x(24-2x)^2$. Note that we must have $0\lt x\lt 12$.
We want to maximize $x(24-2x)^2$, where $x$ ranges over the interval $(0,12)$. The standard technique for this uses the calculus. But you are asking for a procedure that uses a calculator, presumably a graphing calculator. Have the machine graph $x(24-2x)^2$ (over the interval $0\lt x\lt 12$). You should be able to see for what $x$ in this interval the function attains a maximum.