calculus
posted by Yoona on .
1. A sheet of cardboard 3 ft. by 4 ft. will be made into a box by cutting equalsized 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=42h and w=32h
I also distributed them in the equation
I found V= and found the derivative
v'=1228h+12h^2 and I set it equal to zero
from there...I don't know whay to do.

v= h (42h)(32h) = 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