Open Top
2011
If 1300 square centimeters of material is available to make a box with a square base and an open top?
If 1300 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
Volume = cubic centimeters.
How about like this:
let a=sqrt(1300)
Volume = L * W * H
L = a -2x
W = a – 2x
H = x
a
———-
x _| |__x
| | (Ouch Ugly picture hope you get the point)
| |
— —
|______|
So V = (a – 2x) * (a – 2x) * x
so V(x) = x(a – 2x)^2
PRODUCT RULE:
get V’(x) = f(x) * g(x) = f’g + fg’ = 1 * (a – 2x)^2 + x * 2(a – 2x) * (-2)
V’(x) = (a – 2x)^2 -4x * (a – 2x)
V’(x) = (a – 2x)^2 -4x * (a – 2x)
V’(x) = (a – 2x) *( (a – 2x) -4)
Well then get the zero for that V’ which will be a local min / max of V
Solve for x in: 0=(√1300-2x)^2 – 4x(√1300-2x)
Test the zeros for your max
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