let x be length of side of each cut -out square
V = Β x(16 - 2x)(30 - 2x) Β = Β x(480 - 92x + 4x^2)Β = 4x^3 - 92x^2 + 480x
dV/dx = 12x^2 - 184x + 480 Β = 0 for turning points
x = Β 12, 3 .333...
second derivative = 24x - 184
when x = 12 this is positive and when x = 3.33... its negative so we have a maximum when x = 3.33...
Maximum volume Β is Β 3.3333..( 16 - 2(3.33...)(30 - 3.33....)
Β = Β 725.92 in^3
