Surface area of box=1200 cm²
Volume of box=s²h
s = side of square base
h = height of box
S.A. = s² + 4sh
S.A. = surface area or 1200 cm², s²
= the square base, and 4sh = the four 'walls' of the box.
1200 = s² + 4sh
1200 - s² = 4sh
(1200 - s²)/(4s) = h
v(s) = s²((1200 - s²)/(4s))
v(s) = s(1200 - s²)/4 .
v(s) = 300s - (1/4)s^3
by derivating
v'(s) = 300 - (3/4)s²
0 = 300 - (3/4)s²
-300 = (-3/4)s²
400 = s²
s = -20 and 20.
again derivating
v"(s) = -(3/2)s
v"(-20) = -(3/2)(-20)
v"(-20) = 30
v"(20) = -(3/2)(20)
v"(20) = -30
v(s) = 300s - (1/4)s^3
v(s) = 300(20) - (1/4)(20)^3
v(s) = 6000 - (1/4)(8000)
v = 6000 - 2000
v=4000
