{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Input" 2 19 "" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 256 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" 19 260 "" 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 19 261 "" 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier " 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "E rror" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 0 0 0 0 0 0 0 0 0 0 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "M aple Output" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 256 9 "P\370\355klad 6" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "re start;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "Vy\232et\370ete pr\371b\354h funkce" }{TEXT 257 8 " f(x) = " }{XPPEDIT 258 0 "arccsin((1-x^2)/(x^2+1));" "6#-%(arc csinG6#*&,&\"\"\"F(*$%\"xG\"\"#!\"\"F(,&*$F*F+F(F(F(F," }{TEXT -1 0 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "f:=x->arcsin((1-x^2)/(1+x^2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(-%'arcsinG6#*&,&\"\"\"F 1*$)9$\"\"#F1!\"\"F1,&F1F1F2F1F6F(F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Defini\350n\355 obor funkce: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "solve(((1-x^2)/(1+x^2))>=-1 and (1-x^2)/(1+x^2)<=1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"xG" }}} {EXCHG {PARA 256 "" 1 "" {TEXT -1 30 "- jsou to v\232echna re\341ln \341 \350\355sla" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Pr\371se\350 \355ky s osami:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(f(x)=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RootOfG6#--%'arcsinG6#*&,&!\"\"\" \"\"*$)%\"xG\"\"#F-F-F-,&F.F-F-F-F,6#%#_ZG" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 5 "f(0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#--%'arcsinG 6#*&,&\"\"\"F)*$)%\"xG\"\"#F)!\"\"F),&F*F)F)F)F.6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "Sudost resp. lichost funkce:" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 13 "f(-x):=f(-x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"fG6#,$%\"xG!\"\"--%'arcsinG6#*&,&\"\"\"F0*$)F(\"\"#F0F)F0,& F1F0F0F0F)F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "funkce je sud\341 " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "Stacion\341rn\355 body, inter valy monotonie; extr\351my" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "df:=d iff(f(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dfG-%%diffG6$-%\"fG 6#%\"xGF+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "df:=normal(%); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dfG-%%diffG6$-%\"fG6#%\"xGF+" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "Uprav\355me tuto derivaci s ohle dem na hodnotu prom\354nn\351 x" }}{PARA 0 "" 0 "" {TEXT -1 8 "a) x > \+ 0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "assume(x>0):df:=diff(f (x),x);df:=normal(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dfG-%%diff G6$--%'arcsinG6#*&,&\"\"\"F.*$)%#x|irG\"\"#F.!\"\"F.,&F/F.F.F.F36#F1F1 " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dfG,$-%%diffG6$--%'arcsinG6#*&, &!\"\"\"\"\"*$)%#x|irG\"\"#F0F0F0,&F1F0F0F0F/6#F3F3F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "b) x < 0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "assume(x<0):df:=diff(f(x),x);df:=normal(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dfG-%%diffG6$--%'arcsinG6#*&,&\"\"\"F.*$) %#x|irG\"\"#F.!\"\"F.,&F/F.F.F.F36#F1F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dfG,$-%%diffG6$--%'arcsinG6#*&,&!\"\"\"\"\"*$)%#x|irG\"\"#F0F 0F0,&F1F0F0F0F/6#F3F3F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " solve(df);" }}{PARA 8 "" 1 "" {TEXT -1 90 "Error, (in solve) cannot so lve expressions with diff(arcsin((-1+x^2)/(x^2+1))(x),x) for x\n" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 114 "Neexistuje nulov\375 bod 1. deriv ace, v bod\354 x = 0 se v\232ak m\354n\355 jej\355 znam\351nko, nast \341v\341 tedy extr\351m - lok\341ln\355 maximum." }}{PARA 0 "" 0 "" {TEXT -1 57 " Intervaly konvexnosti resp. konk\341vnosti, inflexn\355 \+ body. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dff:=diff(df,x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$dffG,$-%%diffG6$--%'arcsinG6#*&,&! \"\"\"\"\"*$)%#x|irG\"\"#F0F0F0,&F1F0F0F0F/6#F3-%\"$G6$F3F4F/" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 133 "Vypo\350ten\341 derivace plat\355 pro x < 0 , bylo takto naposledy p\370i\370azeno p\370\355kazem assum e, jej\355 znam\351nko je tedy kladn\351, funkce je v tomto " }}{PARA 0 "" 0 "" {TEXT -1 80 "intervalu nad te\350nou. 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