Posted by kim on Sunday, April 29, 2012 at 6:39pm.
v = x(14-2x)(27-2x)
dv/dx = 2(6x^2 - 82x + 189)
dv/dx=0 when x = (41 ± √547)/6 = 2.93, 10.73
knowing the shape of cubics, you should have no trouble "differentiating" the max from the min.
length = z = 27 -2x
width = y = 14 - 2x
v = (27-2x)(14-2x)x
v = ( 378 - 82 x + 4 x^2 ) x
v = 378 x -82 x^2 + 4 x^3
max when dv/dx = 0
dv/dx = 378 - 164 x + 12 x^2 = 0
6 x^2 - 82 x + 189 = 0
x = [ 82 +/- sqrt (6724-4536) ]/12
x = [82 +/- 46.8 ]/12
x = 10.7 too big, negative width
x = 2.93 inches
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