Cdtrjyty

Can anyone give me a clue on how to plot this function:

It can be with any package, as the ones I've tried to use don't work (pgfplots gives me TeX capacity exceeded, sorry), my attempts with other packages aren't even remotely working :(

The graph only has to be in between 0 and 10. Also, is there any way to put a table with the values next to the graph?

Thanks for your help..

documentclass[tikz,border=3.14mm]{standalone}

usepackage{pgfplots}

pgfplotsset{compat=1.16}

begin{document}

begin{tikzpicture}[declare function={myexp(x)=4*(x-1)*exp(-0.5*x)+8;}]

begin{axis}

addplot [domain=0:5] {myexp(x)};

end{axis}

end{tikzpicture}

end{document}

And of course it is possible to add the range from 1 to 10, and to add a table. (You added these requests only after I answer was there.)

documentclass[tikz,border=3.14mm]{standalone}

usetikzlibrary{matrix,calc}

usepackage{pgfplots}

pgfplotsset{compat=1.16}

begin{document}

begin{tikzpicture}[declare function={myexp(x)=4*(x-1)*exp(-0.5*x)+8;}]

begin{axis}

addplot [domain=0:10,samples=101] {myexp(x)};

end{axis}

matrix[matrix of math nodes,anchor=north west,%

column 1/.style={align=right,text width=5mm},

column 2/.style={align=left,text width=8mm}] (mat) at ([xshift=0.2cm]current axis.north

east) {%

x & f(x)\ 

0 & pgfmathparse{myexp(0)}pgfmathprintnumber{pgfmathresult}\ 

1 & pgfmathparse{myexp(1)}pgfmathprintnumber{pgfmathresult}\ 

2 & pgfmathparse{myexp(2)}pgfmathprintnumber{pgfmathresult}\ 

3 & pgfmathparse{myexp(3)}pgfmathprintnumber{pgfmathresult}\ 

4 & pgfmathparse{myexp(4)}pgfmathprintnumber{pgfmathresult}\ 

5 & pgfmathparse{myexp(5)}pgfmathprintnumber{pgfmathresult}\ 

6 & pgfmathparse{myexp(6)}pgfmathprintnumber{pgfmathresult}\ 

7 & pgfmathparse{myexp(7)}pgfmathprintnumber{pgfmathresult}\ 

8 & pgfmathparse{myexp(8)}pgfmathprintnumber{pgfmathresult}\ 

9 & pgfmathparse{myexp(9)}pgfmathprintnumber{pgfmathresult}\ 

10 & pgfmathparse{myexp(10)}pgfmathprintnumber{pgfmathresult}\ 

};

draw ($(mat-1-1.south west)!0.5!(mat-2-1.north west)$) -- 

($(mat-1-2.south east)!0.5!(mat-2-2.north east)$);

draw ($(mat-1-1.north east)!0.5!(mat-1-2.north west)$) -- 

($(mat-12-1.south east)!0.5!(mat-12-2.south west)$);

end{tikzpicture}

end{document}

Note that you can also generate the table in a foreach loop, but I am not going to spell this out here.

run with xelatex

documentclass[pstricks,border=5mm]{standalone}

usepackage{pst-plot}



begin{document}

begin{pspicture}(-1,-1)(11,11)

psaxes{->}(0,0)(-0.5,-0.5)(10,10)[$x$,0][$y$,90]

psplot[algebraic,linecolor=blue,linewidth=2pt]{0}{10}{4*(x-1)*Euler^(-0.5*x)+8}

end{pspicture}

end{document}

A variant with pstricks:

documentclass[11pt, svgnames, border=6pt]{standalone}

usepackage{pst-func}

usepackage{auto-pst-pdf}



begin{document}



begin{pspicture*}(-1.2,-1.2)(11,11)

psset{psgrid, gridcoor ={(0,0)(10,10)}, algebraic}

defF{4*(x-1)*EXP(-x/2) + 8}

psaxes[labels=all, arrows=->, arrowinset=0.1, linecolor=SteelBlue, tickcolor=LightSteelBlue, Dx = 5, Dy = 5, subticks = 5]%

(0,0)(-1,-1)(11,11)[$t$, -120][$y$,-135]

uput[dl](0,0){$ O $}%

psplot[linewidth=1.5pt, linecolor=IndianRed, plotstyle=curve, plotpoints=200]{0}{10}{F}%

psCoordinates[linestyle=dashed, linewidth=0.4pt, linecolor=LightSteelBlue](3, 9.785)

psplotTangent[linecolor=LightSteelBlue]{3}{1}{F}

uput[d](3,0){small$3$}

end{pspicture*}



end{document} 

Quick and dirty attempt with MetaPost, included in a LuaLaTeX program:

RequirePackage{luatex85}

documentclass[border=2mm]{standalone}

usepackage{luamplib}

    mplibsetformat{metafun}

    mplibtextextlabel{enable}

    mplibnumbersystem{double}

begin{document}

begin{mplibcode}

    u := cm; v = .75cm; 

    vardef f(expr t) = 4(t-1)*exp(-.5t) + 8 enddef;

    tmin = -1.25; tmax = 9.75; tstep = .1; ymin = -8.75; ymax = 10.5;

    path curve;

    curve = (tmin, f(tmin))

        for t = tmin + tstep step tstep until tmax+.5tstep: .. (t, f(t)) endfor;

    beginfig(1);

        draw curve xyscaled (u, v);

        drawarrow (tmin*u, 0) -- (tmax*u, 0); drawarrow (0, ymin*v) -- (0, ymax*v);

        for i = ceiling(tmin) upto floor(tmax):

            if i<>0:

                draw (i*u, -2bp) -- (i*u, 2bp);

                label.bot("$" & decimal i & "$", (i*u, 0)); fi

        endfor;

        for j = ceiling(ymin) upto floor(ymax):

            if j<>0:

                draw (2bp, j*v) -- (-2bp, j*v);

                label.lft("$" & decimal j & "$", (0, j*v)); fi

        endfor;

        label.llft("$O$", origin); label.bot("$t$", (tmax*u, 0)); label.lft("$y$", (0, ymax*v)); 

    endfig;

end{mplibcode}

end{document}

If you know R, then knitr is a simple option:

documentclass{article}

begin{document}

<<echo=F,dev="tikz",fig.cap="My function $f(t)=4(t-1)e^{-0.5t}+8$", fig.width=5, fig.height=5, out.width = "\linewidth">>=

t <- seq(0,10,.1)

y <- 4*(t-1)*exp(-0.5*t)+8

plot(t,y,type='l',col='navy', lwd=3,ylab="f(t)",las=1,frame.plot = F, cex.lab=1.2)

@

end{document}

R could also produce the table easily, but place it beside the figure need some tuning of R and LaTeX code:

documentclass{article}

usepackage{booktabs}

begin{document}

begin{figure}

<<xxx, echo=F,dev="tikz", fig.show='hide', fig.width=3, fig.height=3,  out.width = "3in",  out.height="3in">>=

t <- seq(0,10,.1)

y <- 4*(t-1)*exp(-0.5*t)+8

par(mar=c(4.5,4.5,0.5,0))

plot(t,y,type='l',col='navy', lwd=3,ylab="f(t)",las=1,frame.plot = F, cex.lab=1.2)

@

begin{minipage}[t]{3in}vspace{0pt}

includegraphics{figure/xxx-1}

end{minipage}hfill%

begin{minipage}[t]{.2linewidth}smallskip

<<echo=F,results='asis'>>=

x <- seq(0,10)

y <- 4*(x-1)*exp(-0.5*x)+8

df <- data.frame(t=x,f=y)

names(df) <- c("t (time)","Function f(t)")

library(xtable)

print(xtable(df,align=rep("c",3)), include.rownames=F,floating=F, booktabs=T)

@

end{minipage}

caption{My function $f(t)=4(t-1)e^{-0.5t}+8$} 

end{figure}

end{document}