3.1 lokale Steigung und Steigungswinkel

Beispiel $f (x) = \frac{1}{2} x^{2} - 2 x$

Lokale Steignug

\begin{aligned} f^{'} (x) & = x - 2 \\ f^{'} (3) & = 3 - 2 \\ f^{'} (3) & = 1 = m \end{aligned}

Steigungswinkel

\begin{aligned} \tan α = \frac{Gegenkathete}{Ankathete} \\ \tan α = \frac{m}{1} \\ \tan α = 1 |arctan \\ α = 45^{\circ} \end{aligned}

Lokale Steignug

\begin{aligned} f^{'} (x) = x - 2 \\ f^{'} (0) = 0 - 2 \\ f^{'} (0) = - 2 = m \end{aligned}

Steigungswinkel $β$ :

\begin{aligned} \tan β & = \frac{m}{1} \\ \tan β & = - 2 |arctan \\ β & = - 63, 4^{\circ} \end{aligned}