Asked by akash

An open box is to be made from a eighteen-inch by eighteen-inch square piece of material by cutting equal squares from the corners and turning up the sides (see figure). Find the volume of the largest box that can be made.
figure ( a box and one side is 18-2x)
v= ? in^3

Answers

Answered by Steve
v = x(18-2x)^2 = 4x^3-72x^2+324x

Now just find where dv/dx=0 and that will be the maximum (or minimum!) volume. I'm sure you will be able to tell which one.
Answered by akash
so i got x=9 but this is not correct
Answered by Steve
Of course x=9 is incorrect. If you cut off a 9" corner from the 18" square, the volume is zero! Probably not the maximum value.

dv/dx=0 at another value of x. Use that one.
Answered by Anonymous
fight
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