Weg ohne die Ableitung:
Geradenschar durch \(\blue{B(2|9)}\)
\( \frac{y-9}{x-2}=m \) geschnitten mit \(\green{y=4x^2-4x+1}\)
\( \frac{4x^2-4x-8}{x-2}=m \)
\(4x^2-4x-m*x=8-2m \)
\(4x^2-x*(4+m)=8-2m \)
\(x^2-x*(\frac{4+m}{4})=2-\frac{1}{2}m \)
\((x-(\frac{4+m}{8}))^2=2-\frac{1}{2}m+(\frac{4+m}{8})^2 \)
\(x-(\frac{4+m}{8})=\sqrt{2-\frac{1}{2}m+(\frac{4+m}{8})^2} \)
\(\sqrt{2-\frac{1}{2}m+(\frac{4+m}{8})^2}=0 \)
\(2-\frac{1}{2}m+(\frac{4+m}{8})^2=0 \)
\(m=12 \)
Tangente :
\( \frac{y-9}{x-2}=12 \)
\( \blue{y=12x-15} \)