Posted by kim on Sunday, April 29, 2012 at 6:39pm.
a rectangular piece of cardboard measuring 14 inches by 27 inches is to be made into a box with an open top by cutting squares of equal size from each corner and golding up the sides . let x represent the length of a side of each square. for what value of x will the volume be a maximum? round to two decimal places.

precalculus  Steve, Sunday, April 29, 2012 at 6:50pm
v = x(142x)(272x)
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.

precalculus  Damon, Sunday, April 29, 2012 at 6:57pm
length = z = 27 2x
width = y = 14  2x
v = (272x)(142x)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 (67244536) ]/12
x = [82 +/ 46.8 ]/12
x = 10.7 too big, negative width
x = 2.93 inches
Answer This Question
Related Questions
 calculus  an open rectangular box is to be made from a piece of cardboard 8 ...
 Pre Calculus  A piece of cardboard measuring 13 inches by 11 inches is formed ...
 math  A box with an open top is to be constructed from a rectangular piece of ...
 Precalculus  From a rectangular piece of cardboard having dimensions a × b, ...
 calculus optimization problem  by cutting away identical squares from each ...
 Calculus (Optimization)  A rectangular piece of cardboard, 8 inches by 14 ...
 Calculus  An open box is to be made from a rectangular piece of material by ...
 math  a piece of cardboard is twice as it is wide. It is to be made into a box ...
 College Algebra  a box with an open top is constructed from a rectangular piece...
 calc  by cutting away identical squares from each corner of a rectangular piece...
More Related Questions