!!!! fichier de donnees sur la fonction 2 !!!!

!! coefficients pour fabriquer f(x)=log(ax^2+bx+c) !!
a=!randint 1,18
s=!randitem -1,1
b=$[2*$s*$a]
l=!randint 1,9
c=$[$a+($l)^2]

!! formules a faire executer en chaine par maxima !!

f=!exec maxima log($a*x^2+($b)*x+($c));
derf=!exec maxima diff($f,x,1);
1recipf=-($s)-(sqrt((exp(x)-(($l)^2))/($a)))
2recipf=-($s)+(sqrt((exp(x)-(($l)^2))/($a)))
y=log($c)
1derrecipfy=ev($derf,x=-1-($s))
2derrecipfy=ev($derf,x=1-($s))
imborng=ev($f,x=-($s))

!! 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=$[-$s]
pbornd1=$bornd1
delimd1=2
I1=\left$crocd $pborng1,$pbornd1\right$crocd

delimg2=1
borng2=$[-$s]
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=$imborng1
imbornd1=+infinity
pimbornd1=+\infty
imdelimd1=1
imI1=\left$crocg $pimborng1, $pimbornd1\right$crocg

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