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.

Question

figure ( a box and one side is 18-2x)
v= ? in^3

Answer 1

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.

Answer 2

so i got x=9 but this is not correct

Answer 3

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.

Answer 4

fight