it is required to make an open box of gregreatest possible volume from a square piece of tin,whose side is one metre' by cutting equal squares out of the corners and then folding up the tin to form the sides, what should be the length of a side of the sgures cut out/
v = x(1-2x)^2
dv/dx = (x-1)(3x-1)
dv/dx = 0 when x=1 or 1/3
max v at x = 1/3
v(1/3) = 1/3 (2/3)^2 = 4/27