V(x) = [16*10 -16*2x -2x*10 - 2x*(-2x)]*x
= [160 - 32x -20x +4x2]*x
=160x - 52x2 + 4x3
V'(x) = 12x2-104x +160
x2 - 104/12 x + 160/12 = 0
PQ Formel:
x1,2= 104/24 ± √(104/24)^2-160/12)
x1,2 =13/3 ± 7/3
x1 = 6/3 = 2
x2 = 20/3
x2 geht nicht, daher x1 = x = 2 ist die Lösung.
V(2) = (16-4) * (10-4) * 2 = 144