!!!! fichier de donnees sur la fonction 3 !!!!
!! coefficients pour fabriquer exp(ax^2+b) !!
a=!randint 1,19
b=!randint -12,12

f=!exec maxima exp($a*x^2+$b);
derf=!exec maxima diff($f,x,1);

1recipf=-sqrt((log(x)-($b))/($a))
2recipf=sqrt((log(x)-($b))/($a))
y=exp($a+$b)
1derrecipfy=ev($derf,x=-1)
2derrecipfy=ev($derf,x=1)
imborng=exp($b)

!! execution en chaine de maxima puis distribution des resultats !!

dataList=!exec maxima $1recipf;\
$2recipf;\
$y;\
$1derrecipfy;\
$2derrecipfy;\
$imborng;
!distribute lines $dataList into 1recipf,2recipf,y,1derrecipfy,2derrecipfy,imborng

!! forme pour affichage de f(x) !!
pf=!texmath $f

!! les intervalles de monotonie et leurs images !!
!!! intervalles de monotonie !!!
delimg1=2
borng1=-infinity
pborng1=-\infty
bornd1=0
pbornd1=$bornd1
delimd1=2
I1=\left$crocd $pborng1,$pbornd1\right$crocd

delimg2=1
borng2=0
pborng2=$borng2
bornd2=+infinity
pbornd2=+\infty
delimd2=1
I2=\left$crocg $pborng2,$pbornd2\right$crocg
!!! images de I1 et I2 !!!
imdelimg1=1
imborng1=$imborng
pimborng1=!texmath $imborng1
imbornd1=+infinity
pimbornd1=+\infty
imdelimd1=1
imI1=\left$crocg $pimborng1, $pimbornd1\right$crocg

imdelimg2=1
imborng2=$imborng
pimborng2=$imborng2
imbornd2=+infinity
pimbornd2=+\infty
imdelimd2=1
imI2=\left$crocg $pimborng2, $pimbornd2\right$crocg
