500 setwidth
-.5 4.5 setxrange
-.5 6.55 setyrange

0 4.5 setxrange
0 6.55 setyrange

/x1 -1 Exp def
/x2 1 Exp 2 div def
/x3 .5 Exp def
/x4 1 Exp def
/y1 1 Exp 2 mul def

[.5 dup .5 dup .05 dup] {.4 setgray} Quadrillage

/ymarkstyle {cltext} def          %% on centre les marques sur Oy
/axesarrow {} def                 %% on desactive les fleches sur les axes
.7 setlinewidth
tracerepere
marks
0 ymark

<tex>
$\vec \imath $
</tex>
.65 0 [1.5 dup] dctexlabel

<tex>
$\vec \jmath $
</tex>
0 .8 [1.5 dup] cltexlabel

<tex>
$$
   {e\over 2}
$$
</tex>
x2 0 dctexlabel

<tex>
$$
   {1\over e}
$$
</tex>
x1 0 dctexlabel

<tex>
$\sqrt e$
</tex>
x3 0 dctexlabel

<tex>
$e$
</tex>
x4 0 dctexlabel

<tex>
$2e$
</tex>
0 y1 cltexlabel

/f {
   setxvar
   2 x mul
   x ln dup mul 2 mul
   x ln 3 mul sub
   2 add 
   mul
} def
/f' {
   pop 0
} def

1.2 setlinewidth
.0001 xmax {f} Courbe

x2 0 x4 y1 /D defdroite
[x2 0 ymax D ydpoint] ligne

.9 setlinewidth
.7 settailletangente
x1 (f) tangente
x3 (f) tangente

[x1 x2 x3 x4] {xtick} apply
y1 ytick

pointilles
x4 dup f point
[x4 0 x4 dup f 0 y1] ligne
[x1 0 x1 dup f] ligne
[x3 0 x3 dup f] ligne