Hallo Schueler,
A(x) = (a·x2 + b·x + c) / x
Quotientenregel : [ u/v ] ' = [ u ' * v - u * v ' ] / v2
A'(x) = [ (2ax+b) * x - (ax2 + b·x + c) * 1 ] / x2
= (a·x2 - c) / x2 = 0 ⇔x>0 x = √c/√a
A"(x) = [ (2ax * x2 - (a·x2 - c) * 2x ] / x4
= 2·c / x3 → A"( √c/√a) = 2·a3/2 / √c > 0 → Minimalstelle
A(√c/√a) = 2·√a·√c + b
Lage des Minimums: x = √c/√a
Wert des Minimums: 2·√a·√c + b
Gruß Wolfgang