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\documentclass{article} \usepackage{tikz} \usepackage{tikz-3dplot} \usetikzlibrary{math} \usepackage[active,tightpage]{preview} \PreviewEnvironment{tikzpicture} \setlength\PreviewBorder{0.125pt} % % File name: linear-approximation-2d.tex % Description: % The linear approximation for a function of one variable $y = f(x)$ is shown. % % Date of creation: March, 7th, 2021. % Date of last modification: October, 9th, 2022. % Author: Efran Soto Apolinar. % https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/ % Source: page 15 of the % Glosario Ilustrado de Matem\'aticas Escolares. % https://tinyurl.com/5udm2ufy % % Terms of use: % According to TikZ.net % https://creativecommons.org/licenses/by-nc-sa/4.0/ % Your commitment to the terms of use is greatly appreciated. %\begin{document} % \begin{tikzpicture} \pgfmathsetmacro{\xi}{2.5} \pgfmathsetmacro{\step}{1.0} \pgfmathsetmacro{\xf}{\xi+\step} \pgfmathsetmacro{\yi}{exp(0.35*\xi)} \pgfmathsetmacro{\yf}{exp(0.35*\xf)} \pgfmathsetmacro{\yfa}{0.35*exp(0.35*\xi)*(\xf-\xi)+\yi} \pgfmathsetmacro{\ym}{0.5*(\yi+\yfa)} % Coordinate axis \draw[thick,->] (-0.125,0) -- (5,0) node [right]{$x$}; \draw[thick,->] (0,-0.125) -- (0,4.5) node [above]{$y$}; % Graph of the function $y = y(x)$ \draw[red,thick,->] plot[domain=0:4.25] (\x,{exp(0.35*\x)}) node[right]{\footnotesize$y = y(x)$}; % The linear approximation \draw[blue,very thick] (\xi,\yi) -- (\xf,\yfa) -- (\xf,\yi) -- (\xi,\yi); % \draw[dash dot] (\xi,0) node[black,below] {\footnotesize$x$} -- (\xi,\yi) -- (0,\yi) node[left] {\footnotesize$f(x)$}; \draw[dash dot] (\xf,0) node[black,below]{\footnotesize$x + \Delta x$} -- (\xf,\yf) -- (0,\yf) node[left] {\footnotesize$f(x + \Delta x)$}; % Indication of points, measures and lengths \draw[dash dot dot,shift={(\xf,\yi)}] (0,0) -- (2,0); \draw[dash dot dot,shift={(\xf,\yfa)}] (0,0) -- (2,0); \draw[thick,<->,shift={(0,0)}] (\xi,\yi-0.5) -- (\xf,\yi-0.5) node [midway,fill=white] {\footnotesize$\Delta x$}; \draw[thick,<->,shift={(0,0)}] (\xf+1.0,\yi) -- (\xf+1.0,\yfa) node [midway,fill=white] {\footnotesize$f'(x) \cdot \Delta x$}; \draw[thick,<->,shift={(0.55*\xi,0)}] (0,\yi) -- (0,\yf) node [midway,fill=white] {\footnotesize$f(x + \Delta x) - f(x)$}; \draw[thick,<->,shift={(0,0)}] (\xf+1.0,\yi) -- (\xf+1.0,0) node [midway,fill=white] {\footnotesize$f(x)$}; \end{tikzpicture} % \end{document}
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