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  1. f(x) = frac{x^4}{12}-frac{2x^3}{3}+frac{3 x^2}{2}
  2.      
  3. documentclass[tikz,border=3.14mm]{standalone}
  4. usepackage{pgfplots}
  5. pgfplotsset{compat=1.16}
  6. usepgfplotslibrary{fillbetween}
  7. makeatletter
  8. defparsenode[#1]#2pgf@nil{%
  9.     tikzset{label node/.style={#1}}
  10.     defnodetext{#2}
  11. }
  12.  
  13. tikzset{
  14.     add node at x/.style 2 args={
  15.         name path global=plot line,
  16.         /pgfplots/execute at end plot visualization/.append={
  17.             begingroup
  18.             @ifnextchar[{parsenode}{parsenode[]}#2pgf@nil
  19.             path [xshift=-0.1pt,name path global = position line #1-1]
  20.             ({axis cs:#1,0}|-{rel axis cs:0,0}) --
  21.             ({axis cs:#1,0}|-{rel axis cs:0,1});
  22.             path [xshift=0.1pt, name path global = position line #1-2]
  23.             ({axis cs:#1,0}|-{rel axis cs:0,0}) --
  24.             ({axis cs:#1,0}|-{rel axis cs:0,1});
  25.             path [
  26.             name intersections={
  27.                 of={plot line and position line #1-1},
  28.                 name=left intersection
  29.             },
  30.             name intersections={
  31.                 of={plot line and position line #1-2},
  32.                 name=right intersection
  33.             },
  34.             label node/.append style={pos=1}
  35.             ] (left intersection-1) -- (right intersection-1)
  36.             node [label node]{nodetext};
  37.             endgroup
  38.         }
  39.     }
  40. }
  41. makeatother
  42.  
  43. begin{document}
  44.     begin{tikzpicture}[>=latex]
  45.     begin{axis}[
  46.     xtick={-2,-1,...,5},
  47.     xticklabel=empty,
  48.     ytick={-2,-1,...,5},
  49.     yticklabel=empty, grid=major,
  50.     axis x line=center,
  51.     axis y line=center,
  52.     xlabel={$x$},
  53.     ylabel={$y$},
  54.     xlabel style={below},
  55.     ylabel style={left},
  56.     xmin=-2,
  57.     xmax=5,
  58.     ymin=-2,
  59.     ymax=5,
  60.     tangent/.style={
  61.         add node at x={#1}{
  62.             [
  63.             sloped,
  64.             append after command={(tikzlastnode.west) edge [thick,black] (tikzlastnode.east)},
  65.             minimum width=0.2textwidth
  66.             ]
  67.         }      
  68.     }]
  69.     addplot[color=blue,smooth,samples=501, thick,tangent/.list={1,3},domain=-5:5] {(3* x^2)/2 - (2 *x^3)/3 + x^4/12};
  70.     end{axis}
  71.     end{tikzpicture}
  72. end{document}
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