rectangular open-topped box is made from a 9 x 16 piece of cardboard by cutting x-inch squares out of each corner and folding up the sides.

Question

What size square should be cut out to produce a volume of 120 cubic inches??

I set it up with
120 = (16-2x)(9-2x)(x)
I get to
y = 2x^3 - 25x^2 +72x -60 and I'm stuck. Where do I go from here?

Answer 1

Let the corner pieces be x by x.

Then, x(16 - 2x)(9 - 2x) = 120

144x - 50x^2 + 4x^3 = 120

4x^3 - 50x^3 + 144x - 120 = 0

2x^3 - 25x^2 + 72x - 60 = 0

First derivative =

6x^2 - 50x + 72 = 0

3x^2 - 25x + 36 = 0

x = [25+/-sqrt(25^2 - 4(3)36)]/6

x = 1.851

Answer 2

I don't know calculus. I'm still in algebra. please explain