fa(x) = 1/6·x^3 - a^2/4·x^2
ga(x) = -1/a·x^2 + 3·a/2·x
a)
Nullstellen
fa(x) = 1/6·x^3 - a^2/4·x^2 = 0 --> x = 1.5·a^2 ∨ x = 0
ga(x) = -1/a·x^2 + 3/2·a·x = 0 --> x = 1.5·a^2 ∨ x = 0
b)
ga'(x) = 1.5·a - 2/a·x = 0 --> x = 0.75·a^2
ga(0.75·a^2) = 0.5625·a^3 → HP(0.75·a^2 | 0.5625·a^3)
0.5625·a^3 > 4.5 --> a > 2
Versuche obiges erstmal nachzuvollziehen und zu verstehen.