Question

THE DREADED CALCULUS HELP We want to make a box using a piece of cardboard that is 12 inches along each side. To form the box, we cut squares at each corner and then fold up the sides. What will be the dimensions (l*w*h) of the box with the maximum volume?

Answer 1

I'm not in calculus and I will probably get this wrong.. sorry. :( I tried.

Answer 2

if x = amount cut
then x = height = h
L = W = 12 - 2h

so A = h(12-2h)(12-h)
and take the derivative of that

Answer 3

whoops * h(12-2h)(12-2h)

Answer 4

I think you are on the right track, but i'm not quite sure about how to get that. It's supposed to be answer in l*w*h form, so i don't think we're looking for just a number, specifically.

Answer 5

h(12-2h)(12-2h)
= h(144 - 48h + 4h^2)
= 4h^3 - 48h^2 + 144h <-- take derivative of that

Answer 6

I come up with 12h2−96h+144

Answer 7

let me see if i can hold on a sec.

Answer 8

yep :)
now find h when 12h^2 - 96h + 144 =0

Answer 9

is it 2 or 6? i got 2 answers. haha im so lost.

Answer 10

yeah that's right
but you have to use common sense now :)
what happens when you cut two squares of length 6 from a length of 12?
0
so 6 won't work

so you'll be left with amount cut out = x = h = 2

Answer 11

so, how could we put that in l*w*h form?

Answer 12

so we got that h = 2
then L = W = 12 - 2h
plug in h to get L and W

Answer 13

12-4=8 right?

Answer 14

yep so "l*w*h" = 8*8*2 =

Answer 15

8*8*2=128?

Answer 16

Thank you, jigglypuff314.

Answer 17

you're welcome :)

Answer 18

but I would just suggest you not ask me Calc questions in the future xD
I'm just learning it myself :P and am failing utterly... so... yeah....