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{SECT 0 {EXCHG {PARA 265 "" 0 "" {TEXT 271 35 "Matematick\351 v\375po
\350ty se syst\351m Maple" }}}{EXCHG {PARA 266 "" 0 "" {TEXT -1 77 "au
tor:  Ing. Vladim\355r \216\341k\n  email:  zakyn@centrum.cz\n        \+
         web:   " }{URLLINK 17 "www.vladimirzak.com/maple" 4 "www.vlad
imirzak.com/maple" "" }}{PARA 265 "" 0 "" {TEXT -1 0 "" }}{PARA 265 "
" 0 "" {TEXT -1 12 "            " }{TEXT 269 9 "recenzent" }{TEXT -1 
3 ":  " }{TEXT 268 31 "Prof. RNDr. Ji\370\355 H\370eb\355\350ek, CSc.
" }}{PARA 265 "" 0 "" {TEXT -1 48 "CENTRUM BIOSTATISTIKY A ANAL\335Z (
CBA LF a P\370F MU)" }}{PARA 265 "" 0 "" {TEXT -1 43 "L\351ka\370sk
\341 a P\370\355rodov\354deck\341 fakulta MU v Brn\354" }}{PARA 265 "
" 0 "" {TEXT -1 20 "hrebicek@cba.muni.cz" }}{PARA 265 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 265 "" 0 "" {TEXT -1 478 "Tento dokument je ur
\350en jen pro v\375ukov\351 \372\350ely a pro pou\236it\355 jen osoba
mi, kter\375m byl tento dokument poskytnut p\370\355mo autorem, pop
\370. si ho st\341hli z webov\351ho s\355dla autora. Jak\351koliv \350
\341sti dokumentu nen\355 mo\236n\351 pou\236\355t bez citace zdoje, t
edy n\341zvu dokumentu a jm\351na autora s kontaktn\355mi informacemi \+
(jak je zobrazeno v hlavi\350ce), kter\341 mus\355 b\375t autorovi sd
\354lena. Pro jin\351 pou\236it\355 ne\236 pro osobn\355 pot\370eby os
ob, tedy pro distribuci \350i kop\355rov\341n\355, je nutn\351 obdr
\236et p\355semn\375 souhlas autora. " }}{PARA 265 "" 0 "" {TEXT -1 0 
"" }}{PARA 265 "" 0 "" {TEXT -1 0 "" }{TEXT 270 59 "Soubor vznikl s po
dporou grantov\351ho projektu FRV\212 3323/2006" }{TEXT -1 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 14 "Extr\351m
y funkce" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 187 "Syst\351m Maple obsah
uje p\370\355kazy pro v\375po\350et extr\351m\371 jak voln\375ch tak i
 v\341zan\375ch rovnicemi (nerovnicemi) a m\371\236e velmi pomoci p
\370i \370e\232en\355 \372loh hled\341n\355 extr\351m\371 funkc\355 je
dn\351 nebo v\355ce prom\354nn\375ch." }}{PARA 0 "" 0 "" {TEXT -1 78 "
Pro v\375po\350et minim\341ln\355 hodnoty funkce jedn\351 \350i v\355c
e prom\354nn\375ch je ur\350en p\370\355kaz " }{TEXT 257 8 "minimize" 
}{TEXT -1 41 " a pro nalezen\355 maxim\341ln\355 hodnoty p\370\355kaz \+
" }{TEXT 256 8 "maximize" }{TEXT -1 328 ". Po\350\355t\341me-li voln
\351 glob\341ln\355 minimum (maximum) funkce, zad\341me pouze funkci, \+
tzn. p\370\355kazy maj\355 jeden parametr. V p\370\355pad\354 omezen
\355 pomoc\355 rovnic zad\341me tato omezen\355 jako dal\232\355 param
etr. Pomoc\355 interval\371 lze tak\351 specifikovat oblast, ve kter
\351 extr\351m hled\341me. Oba p\370\355kazy vyp\355\232\355 hodnotu m
inima (maxima) dan\351 funkce. Pomoc\355 parametru " }{TEXT 258 8 "loc
ation" }{TEXT -1 63 " bude v\375pis roz\232\355\370en o sou\370adnice \+
bod\371, v nich\236 extr\351m nast\341v\341." }}{PARA 0 "" 0 "" {TEXT 
-1 49 "N\341sleduj\355c\355 p\370\355klady uk\341\236\355 pou\236it
\355 t\354chto p\370\355kaz\371" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 25 "f:=x*y*exp(-(x^2+y^2)/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%\"fG*(%\"xG\"\"\"%\"yGF'-%$expG6#,&*&\"\"#!\"\"F&F.F/*&F.F/F(F.F/F'" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "maximize(%,location);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$-%$expG6#!\"\"<$7$<$/%\"xG\"\"\"/%\"yG
F,F#7$<$/F+F&/F.F&F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "min
imize(%%,location);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$-%$expG6#!\"
\"F'<$7$<$/%\"xG\"\"\"/%\"yGF'F#7$<$/F/F-/F,F'F#" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 48 "Na dal\232\355m p\370\355kladu uk\341\236eme speci
fikaci interval\371" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "mini
mize(x^2-3*x+y^2*x+3,location);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$%
)infinityG!\"\"<$7$<$/%\"xG-%)INTERVALG6#;F#\"\"!/%\"yGF#F#7$<$F)/F1F$
F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "minimize(x^2-3*x+y^2*
x+3,x=0..2,y=0..2,location);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$#\"\"$
\"\"%<#7$<$/%\"xG#F$\"\"#/%\"yG\"\"!F#" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 115 "Dal\232\355 p\370\355klad uk\341\236e omezen\355 t\354ch
to p\370\355kaz\371. Maple neum\355 pomoc\355 t\354chto p\370\355kaz
\371 nal\351zt extr\351m funkce na dan\351 mno\236in\354 " }{TEXT 259 
1 "M" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f1:
=x^2-y^2+4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1G,(*$)%\"xG\"\"#\"
\"\"F**$)%\"yGF)F*!\"\"\"\"%F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 13 "M:=x^2+y^2=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG/,&*$)%
\"xG\"\"#\"\"\"F+*$)%\"yGF*F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "maximize(f1,M);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%
)maximizeG6$,(*$)%\"xG\"\"#\"\"\"F+*$)%\"yGF*F+!\"\"\"\"%F+/,&F'F+F,F+
F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "minimize(f1,M);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%)minimizeG6$,(*$)%\"xG\"\"#\"\"\"F+*
$)%\"yGF*F+!\"\"\"\"%F+/,&F'F+F,F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 115 "Proto je v Maple k dispozici dal\232\355 p\370\355kaz ur\350en
\375 pro hled\341n\355 extr\351m\371 funkc\355 jedn\351 \350i v\355ce \+
prom\354nn\375ch. Jde o p\370\355kaz " }{TEXT 260 7 "extrema" }{TEXT 
-1 60 ", kter\375 hled\341 extr\351my metodou Lagrangeov\375ch multipl
ik\341tor\371. " }}{PARA 0 "" 0 "" {TEXT 261 55 "extrema(v\375raz, \{o
mezen\355\}, \{ prom\354nn\351 \}, ' sou\370adnice ')" }}{PARA 0 "" 0 
"" {TEXT -1 502 "Posledn\355 parametr je nepovinn\375, ale specifikuje
 \370et\354zec, do kter\351ho budou ulo\236eny sou\370adnice bod\371, \+
v nich\236  nast\341v\341 maximum a minimum.\nTento p\370\355kaz neroz
li\232uje mezi minimy a maximy, hled\341 oba extr\351my. D\355ky speci
fikaci prom\354nn\375ch m\371\236eme tento p\370\355kaz u\236\355t tak
\351 p\370i hled\341n\355 extr\351m\371 funkce s parametry, kdy pro n
\354kterou hodnotu parametru nab\375v\341 funkce maxima a pro jinou mi
nima. V p\370\355pad\354 hled\341n\355 voln\351ho extr\351mu, tj. nejs
ou \236\341dn\351 omezuj\355c\355 podm\355nky, je nutn\351 zadat druh
\375 parametr v podob\354 pr\341zdn\351 mno\236iny." }}{PARA 0 "" 0 "
" {TEXT -1 79 "Pou\236it\355 tohoto p\370\355kazu uk\341\236eme na ji
\236 zm\355n\354n\351m p\370\355kladu. Hled\341me extr\351my funkce" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "f1;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"F(*$)%\"yGF'F(!\"\"\"\"%F(" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "na mno\236in\354" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 2 "M;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*
$)%\"xG\"\"#\"\"\"F)*$)%\"yGF(F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "extrema(f1,\{M\},\{x,y\},'body');" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#<$\"\"$\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 5 "body;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&<$/%\"xG\"\"!/%\"yG\"
\"\"<$F%/F)!\"\"<$/F)F'/F&F-<$F//F&F*" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 308 "Pro \372plnost uve\357me je\232t\354 p\370\355pad, kdy j
e extr\351m v\341z\341n omezuj\355c\355mi podm\355nka ve tvaru nerovni
c. V tomto p\370\355pad\354 syst\351m Maple poskytuje podporu pro line
\341rn\355 funkce v\355ce prom\354nn\375ch a pro omezen\355 ve tvaru n
erovnic. \330e\232en\355 v\232ak nen\355 zalo\236eno na prost\370edc
\355ch matematick\351 anal\375zy a je obsa\236eno v roz\232i\370uj\355
c\355 knihovn\354 " }{TEXT 262 7 "simplex" }{TEXT -1 45 ". V\355ce inf
ormac\355 naleznete na doprovodn\351m CD." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
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