Buongiorno a tutti.
Ho il seguente disegno:
`\documentclass{article}
\usepackage{tikz,pgfplots,xcolor}
\begin{document}
\begin{tikzpicture}[font=\small]
\begin{axis} [width=0.8\textwidth,
axis lines=middle,
xmin=-0.25,xmax=5,ymin=-1,ymax=10,
enlargelimits,
xtick=\empty,
ytick={2,8},
yticklabels={$f(a)$,$f(a+h)$},
xlabel=$x$,
ylabel=$y$]
\draw [dashed] (axis cs:1,-1.5) — (axis cs:1,2);
\draw [dashed] (axis cs:4.75,2) — (axis cs:0,2);
\draw [dashed] (axis cs:3,-1.5) — (axis cs:3,8);
\draw [dashed] (axis cs:4.75,8) — (axis cs:0,8);
\draw [dashed,latex-latex] (axis cs:4,2) — (axis cs:4,8);
\draw [dashed,latex-latex] (axis cs:1,-1) — (axis cs:3,-1);
\addplot [domain=-5:5, samples=200, restrict y to domain=-30:30,smooth,very thick] {2^x};
\addplot [domain=-5:5, samples=200, restrict y to domain=-30:30,smooth] {2*x};
\addplot [domain=-5:5, samples=200, restrict y to domain=-30:30,smooth,green] {3*x-1};
\addplot [domain=-5:5, samples=200, restrict y to domain=-30:30,smooth,thick,red] {1.386294361*x+0.613705639};
\begin{scope}[text height=1ex, text depth=0pt]
\node [below right] at (axis cs:1,0) {$a$};
\node [below right] at (axis cs:3,0) {$a+h$};
\end{scope}
\node [above=2pt] at (axis cs:1,2) {$P$};
\node [above left] at (axis cs:3,8) {$Q$};
\node
at (axis cs:4,5) {$f(a+h)-f(a)$};
\node [below] at (axis cs:2,-1) {$h$};
\node [below] at (axis cs:3,4) {\color{red}retta tangente};
\node [below] at (axis cs:4.35,10.5) {rette secanti};
\node [below] at (axis cs:2.85,10.5) {\color{blue}$y=f(x)$};
\draw (axis cs:1,2) [blue,fill=blue,very thick] circle (2.0pt);
\draw (axis cs:2,4) [blue,fill=blue,very thick] circle (2.0pt);
\draw (axis cs:3,8) [blue,fill=blue,very thick] circle (2.0pt);
%\draw (axis cs:1,2) ++(54.195:40mm) arc (54.195:71.56:40mm);
\end{axis}
\end{tikzpicture}
\end{document}`
Vorrei aggiungere un bell’arco di circonferenza di centro P(1,2) che colleghi le retta (secante, in verde) $y=3x-1$ con la retta (tangente, in rosso) $y=2\ln 2 x+2-\ln 2$, quest’ultima approssimativamente uguale a $y=1.38x+0.61$. Ho fatto i calcoli e gli angoli dovrebbero essere 54.195 gradi e 71.565 gradi.
Non ci riesco.
Qualcuno mi aiuta?
Grazie anticipate! 🙂