3.5 Berührung zweier Graphen

Bedingung für B:

\begin{aligned} I f (x_{B}) = g (x_{B}) \\ II f^{''} (x_{B}) = g^{'} (x_{B}) \end{aligned}

\begin{array}{lllll} f (x) = x^{2} + 2 & f^{'} (x) = 2 x & f (1) = 3 & g (1) = 3 \\ g (x) = 4 x - x^{2} & g^{'} (x) = 4 - 2 x & f^{'} (1) = 2 & g (1) = 2 \end{array}

$B (1 / f (1))$

\begin{aligned} f (x) & = g (x) \\ x^{2} + 2 & = 4 x - x^{2} & ∣ + x^{2} ∣ - 4 x \\ 2 x^{2} + 4 x + 2 & = 0 & ∣: 2 \\ x^{2} + 2 x + 1 & = 0 \\ x_{1 / 2} & = 1 \pm \sqrt{1 - 1} \\ x_{1 / 2} & = 1 (dopellte Schnittstelle) ⟹ Die Graphen berühren sich \end{aligned}