Question

Find the largest volume of the open box to be made from cutting equal squares from 3m by 8m sheet then folding it up.

Answer 1

size of cut-out squares:
x by x m
V = x(3-2x)(8-3x), 0 < x < 3/2
= x(24 - 25x + 6x^2)
= 24x - 25x^2 + 6x^3

dV/dx = 24 - 50x + 18x^2
= 0 for a max of V
9x^2 - 25x + 12 = 0

by formula I got x = .617 and 2.16 , reject the 2.16 since it will
produce a negative dimension

Sub that into V = ...
to find that max volume

check my arithmetic