Question

1. A sheet of cardboard 3 ft. by 4 ft. will be made into a box by cutting equal-sized squares from each corner and folding up the four edges. What will be the dimensions of the box with largest volume?

so I did V=lhw
and found l=4-2h and w=3-2h
I also distributed them in the equation
I found V= and found the derivative
v'=12-28h+12h^2 and I set it equal to zero
from there...I don't know whay to do.

Answer 1

v= h (4-2h)(3-2h) = h (12 - 14 h + 4 h^2)
v = 12 h - 14 h^2 + 4 h^3
0 = 12 - 28 h + 12 h^2 agreed now factor 4 out
3 h^2 -7 h + 3 = 0
h = [ 7 +/- sqrt(49 - 36) ]/6
= [ 7 +/- sqrt(13)]/6
= 1.77 or .566
1.77 is more than half the width of 3 so is no good
use h = 0.566