calculus

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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.

  • calculus -

    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

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