Math problem

Question

From a 15-inch by 15-inch piece of metal, squares are cut out of the four corners so that the sides can then be folded up to make a box. Let x represent the length of the sides of the squares, in inches, that are cut out. Express the volume of the box as a function of x. Graph the function and from the graph determine the value of x, to the nearest tenth of an inch, that will yield the maximum volume.

Answer 1

v= x(15-2x)^2

= 225x -30x^2 +4x^3

v'=12x^2 -60x +225=0

x=60/24 +/-(1/24)sqr(3600-48(12))

x=2.5 +/-(sqr3024)/24

= almost 2.5 - 55/24

= about 2.5+/- 2.3

= .2 or 4.8

v=.2(14.8)^2 or 4.8(10.2)^2

4.8(10.2^2 >.2(14.8)^2

x=4.8 inches