Abschnittsweise definierte Funktionen

f (x) = a x^{3} + b x^{2} + c x + d

f^{'} (x) = 3 a x^{2} + 2 b x + c

Bedingungen:

{\begin{cases} f (0) = 0 \\ f^{'} (0) = \frac{d}{d x} \tan (38) \\ f (30) = - 15 \\ f^{'} (30) = \frac{d}{d x} \tan (10) * 30 \end{cases}

Gleichungssystem

{\begin{cases} d = 0 \\ c = \frac{d}{d x} \tan (38) \\ a * 30^{3} + b * 30^{2} + c * 30 + d = - 15 \\ 3 a * 30^{2} + 2 b * 30 + c = \frac{d}{d x} \tan (10) * 30 \end{cases}

CAS solve:

\begin{matrix} a = c \\ b = \frac{1 + 60 a}{2} \\ c = 0 \\ d = 0 \end{matrix}

f (x) = x^{3} + \frac{61}{2} x^{2}