{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 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 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "priklad:=\"01\";Digi ts:=30;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(prikladGQ#016\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'DigitsG\"#I" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 193 "xznacky:=proc(sezx)\nlocal tmp,i;\ntmp:=\{\}; \nfor i from 1 by 1 to nops(sezx) do\ntmp:=tmp union \{line([sezx[i],- 1],[sezx[i],1],linestyle=1,thickness=1,color=black)\};\nend do;\nretur n(tmp);\nend proc;\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(xznackyGf*6 #%%sezxG6$%$tmpG%\"iG6\"F+C%>8$<\"?(8%\"\"\"F2-%%nopsG6#9$%%trueG>F.-% &unionG6$F.<#-_%*plottoolsG%%lineG6'7$&F66#F1!\"\"7$FCF2/%*linestyleGF 2/%*thicknessGF2/%&colorG%&blackGOF.F+F+F+" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 197 "yznacky:=proc(sezx)\nlocal tmp,i;\ntmp:=\{\};\nfor i from 1 by 1 to nops(sezx) do\ntmp:=tmp union \{line([-0.1,sezx[i]], [0.1,sezx[i]],linestyle=1,thickness=1,color=black)\};\nend do;\nreturn (tmp);\nend proc;\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(yznackyGf*6# %%sezxG6$%$tmpG%\"iG6\"F+C%>8$<\"?(8%\"\"\"F2-%%nopsG6#9$%%trueG>F.-%& unionG6$F.<#-_%*plottoolsG%%lineG6'7$$!\"\"FD&F66#F17$$F2FDFE/%*linest yleGF2/%*thicknessGF2/%&colorG%&blackGOF.F+F+F+" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 183 "box:=proc(x,y) \n`if`(type(x,realcons) and ty pe(y,realcons),\{line([0,y],[x,y],linestyle=3,thickness=1,color=black) ,line([x,0],[x,y],linestyle=3,thickness=1,color=black)\},\{\});\nend p roc;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$boxGf*6$%\"xG%\"yG6\"F)F)-% #ifG6%3-%%typeG6$9$%)realconsG-F/6$9%F2<$-_%*plottoolsG%%lineG6'7$\"\" !F57$F1F5/%*linestyleG\"\"$/%*thicknessG\"\"\"/%&colorG%&blackG-F86'7$ F1F=F>F?FBFE<\"F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "j ednotky:=proc(x,y)\n\{line([-0.1,y],[0.1,y],linestyle=1,thickness=1,co lor=black),line([x,-0.1],[x,0.1],linestyle=1,thickness=1,color=black) \}\nend proc;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)jednotkyGf*6$%\"xG %\"yG6\"F)F)<$-_%*plottoolsG%%lineG6'7$$!\"\"F29%7$$\"\"\"F2F3/%*lines tyleGF6/%*thicknessGF6/%&colorG%&blackG-F,6'7$9$F17$FAF5F7F9F;F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f:=x->x^3+3*x^2-9*x-10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arr owGF(,**$)9$\"\"$\"\"\"F1*&F0F1)F/\"\"#F1F1*&\"\"*F1F/F1!\"\"\"#5F7F(F (F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "df:=unapply(combine( simplify(D(f)(x)),power),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dfG f*6#%\"xG6\"6$%)operatorG%&arrowGF(,(*&\"\"$\"\"\")9$\"\"#F/F/*&\"\"'F /F1F/F/\"\"*!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " d2f:=unapply(combine(simplify(D(df)(x)),power),x);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%$d2fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(,&*&\"\"'\" \"\"9$F/F/F.F/F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 195 "_n ulove_body_f:=\{solve(f(x)=0,x)\};_nulove_body_df:=\{solve(df(x)=0,x) \};_nulove_body_d2f:=\{solve(d2f(x)=0,x)\};stac_body:=\{seq([_nulove_b ody_df[i],f(nulove_body_df[i])],i=1..nops(_nulove_body_df))\};" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%/_nulove_body_fG<%,(*&\"\"#!\"\",&\" \"%F)*&^#F+\"\"\"\"$b##F.F(F.#F.\"\"$F.*&\"\")F.F*#F)F2F.F.F),**&F+F)F *F1F)*&F+F.F*F5F)F.F)*(^##F)F(F.F2F0,&*&F(F)F*F1F.*&F4F.F*F5F)F.F.,**& F+F)F*F1F)*&F+F.F*F5F)F.F)*(^#F0F.F2F0F%0_nulove_body_dfG<$!\"$\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%1_nulove_body_d2fG<#!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*stac_bodyG<$7$!\"$\"#<7$\"\"\"!#:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 616 "nulove_body_f:=\{\}:evalf(_nulove_body_f ):\nfor i from 1 by 1 to nops(_nulove_body_f) do\n\nnulove_body_f:=nul ove_body_f union `if`(typematch(_nulove_body_f[i],realcons),\{_nulove_ body_f[i]\},\{\});\nend do:\n\nnulove_body_df:=\{\}:evalf(_nulove_body _df):\nfor i from 1 by 1 to nops(_nulove_body_df) do\n\nnulove_body_df :=nulove_body_df union `if`(typematch(_nulove_body_df[i],realcons),\{_ nulove_body_df[i]\},\{\});\nend do:\n\nnulove_body_d2f:=\{\}:evalf(_nu love_body_d2f):\nfor i from 1 by 1 to nops(_nulove_body_d2f) do\n\nnul ove_body_d2f:=nulove_body_d2f union `if`(typematch(_nulove_body_d2f[i] ,realcons),\{_nulove_body_d2f[i]\},\{\});\nend do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "nulove_body_f;evalf(nulove_body_f);evalf(nulove_body_df);evalf(nul ove_body_d2f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$$!\"$\"\" !$\"\"\"F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#$!\"\"\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 204 "f_rostouci:=x->piecewise(df (x)>0,f(x),infinity);\nf_klesajici:=x->piecewise(df(x)<0,f(x),infinity );\ndf_rostouci:=x->piecewise(d2f(x)>0,df(x),infinity);\ndf_klesajici: =x->piecewise(d2f(x)<0,df(x),infinity);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+f_rostouciGf*6#%\"xG6\"6$%)operatorG%&arrowGF(-%*pie cewiseG6%2\"\"!-%#dfG6#9$-%\"fGF3%)infinityGF(F(F(" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%,f_klesajiciGf*6#%\"xG6\"6$%)operatorG%&arrowGF(-%* piecewiseG6%2-%#dfG6#9$\"\"!-%\"fGF2%)infinityGF(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,df_rostouciGf*6#%\"xG6\"6$%)operatorG%&arrowGF( -%*piecewiseG6%2\"\"!-%$d2fG6#9$-%#dfGF3%)infinityGF(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-df_klesajiciGf*6#%\"xG6\"6$%)operatorG%&arro wGF(-%*piecewiseG6%2-%$d2fG6#9$\"\"!-%#dfGF2%)infinityGF(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 152 "f_konkavni:=x->piecewise(d2 f(x)>0,f(x),infinity);\nf_konvexni:=x->piecewise(d2f(x)<0,f(x),infinit y);\nd2f_kladna:=x->piecewise(d2f(x)>0,d2f(x),infinity);\n" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+f_konkavniGf*6#%\"xG6\"6$%)o peratorG%&arrowGF(-%*piecewiseG6%2\"\"!-%$d2fG6#9$-%\"fGF3%)infinityGF (F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+f_konvexniGf*6#%\"xG6\"6$% )operatorG%&arrowGF(-%*piecewiseG6%2-%$d2fG6#9$\"\"!-%\"fGF2%)infinity GF(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+d2f_kladnaGf*6#%\"xG6\"6 $%)operatorG%&arrowGF(-%*piecewiseG6%2\"\"!-%$d2fG6#9$F1%)infinityGF(F (F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 234 "lokalni_minima:=\{ \}:\nfor i from 1 by 1 to nops(nulove_body_df) do\ntmp:=`if`(evalf(d2f (nulove_body_df[i]))>0,\{[evalf(nulove_body_df[i]),evalf(f(nulove_body _df[i]))]\},\{\}):\nlokalni_minima:=lokalni_minima union tmp:\nend do: \nlokalni_minima;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#7$$\"\"\"\"\"!$ !#:F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 234 "lokalni_maxima:= \{\}:\nfor i from 1 by 1 to nops(nulove_body_df) do\ntmp:=`if`(evalf(d 2f(nulove_body_df[i]))<0,\{[evalf(nulove_body_df[i]),evalf(f(nulove_bo dy_df[i]))]\},\{\}):\nlokalni_maxima:=lokalni_maxima union tmp:\nend d o:\nlokalni_maxima;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#7$$!\"$\"\"!$ \"# " 0 "" {MPLTEXT 1 0 194 "inflexe:=\{\}:\n for i from 1 by 1 to nops(nulove_body_df) do\ntmp:=`if`(evalf(d2f(nulo ve_body_df[i]))=0.0,\{[nulove_body_df[i],f(nulove_body_df[i])]\},\{\}) :\ninflexe:=inflexe union tmp:\nend do:\ninflexe;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 346 "fx_m in:=-5;fx_max:=3;fy_min:=-15.5;fy_max:=17.5;\ndfx_min:=fx_min;dfx_max: =fx_max;\nd2fx_min:=fx_min;d2fx_max:=fx_max;\ndfy_min:=-12.5;dfy_max:= 36.5;\nd2fy_min:=-24.5;d2fy_max:=24.5;\n\nlimit(f(x),x=infinity);\nlim it(df(x),x=infinity);\nlimit(d2f(x),x=infinity);\n\nwith(plots):\nseto ptions(tickmarks=[0,0],titlefont=[TIMES,ROMAN,16],scaling=UNCONSTRAINE D):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'fx_minG!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'fx_maxG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%'fy_minG$!$b\"!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'fy_maxG$ \"$v\"!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(dfx_minG!\"&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%(dfx_maxG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)d2fx_minG!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%) d2fx_maxG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(dfy_minG$!$D\"!\" \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(dfy_maxG$\"$l$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)d2fy_minG$!$X#!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)d2fy_maxG$\"$X#!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)infinityG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%)infinityG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "minimize(df(x),x=fx_min..fx_max);maximize(df(x),x= fx_min..fx_max);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!#7" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#\"#O" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "minimize(d2f(x),x=fx_min..fx_max);maximize(d2f(x),x=fx_min..fx_max );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!#C" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#C" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 327 "cary_f:=xznacky([-3,1]) uni on yznacky([-15,17]):\nwith(plottools):\nfor i from 1 by 1 to nops(nul ove_body_df) do\ntmp:=nulove_body_df[i]:\ncary_f:=cary_f union box(eva lf(tmp),evalf(f(tmp))):\nend do:\ngraf_f:=\{plot([f_rostouci(x),f(x)], x=fx_min..fx_max,y=fy_min..fy_max,numpoints=400,color=[blue,red],thick ness=[3,2])\} union cary_f:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 319 "cary_df:=xznacky( [-1]) union yznacky([-12]):\n\nfor i from 1 by 1 to nops(nulove_body_d 2f) do\ntmp:=nulove_body_d2f[i]:\ncary_df:=cary_df union box(evalf(tmp ),evalf(df(tmp))):\nend do:\ngraf_df:=\{plot([df_rostouci(x),df(x)],x= dfx_min..dfx_max,y=dfy_min..dfy_max,color=[blue,red],discont=true,thic kness=[3,2])\} union cary_df:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 189 "cary_d2f:=xznacky([-1]) union yznacky([6]);\ngraf_d2f:=\{plot ([d2f_kladna(x),d2f(x)],x=d2fx_min..d2fx_max,y=d2fy_min..d2fy_max,colo r=[green,red],thickness=[3,2],discont=true)\} union cary_d2f:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6# >%)cary_d2fG<$-%'CURVESG6&7$7$$!\"\"\"\"!F+7$F+$\"\"\"F--%'COLOURG6&%$ RGBG$F-F-F5F5-%*LINESTYLEG6#F0-%*THICKNESSGF8-F'6&7$7$$F,F,$\"\"'F-7$$ F0F,F@F1F6F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "fsolve(f(x) =0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%$!?W)p(*3#o5$*)>YsR]]%!#H$!? IqaIkP*G3#RuN=m\"*!#I$\"?ZX#Gt>'R,\"f?3e;U#F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "with(plots):plotsetup(default);display(graf_f);d isplay(graf_df);display(graf_d2f);" }}{PARA 13 "" 0 "" {TEXT -1 0 "" } }{PARA 13 "" 1 "" {GLPLOT2D 632 497 497 {PLOTDATA 2 "61-%'CURVESG6&7$7 $$!\"$\"\"!$!\"\"F*7$F($\"\"\"F*-%'COLOURG6&%$RGBG$F*F*F4F4-%*LINESTYL EG6#F/-%*THICKNESSGF7-F$6&7$7$F(F47$F($\"#F0FAF8-F$6&7$7$F.F+7$F.F.F0F5F8-F$6&7$7$F.F4FVF0FAF 8-F$6%7_x7$$!\"&F*FI7$$!?s(3NShX#)H>xGA!z\\!#H$!?a0)ptTj)[+$**Q2]U\"!# G7$$!?Vs*)eNUpx5V#pp2'\\Fgo$!?C?$>(44mq!zbn61O\"Fjo7$$!?0?!3KG8`7]+uU- %\\Fgo$!?'zbkerbme?9kP\"*G\"Fjo7$$!?q\"os!H;lgUq@(z&>\\Fgo$!?GX'4vk'or xM#*e>=7Fjo7$$!?3JC(*)eNUpx5\"\\,**[Fgo$!?%3I#p35%*3pA\"G)e[6Fjo7$$!?: fOY&=u'py9*p[*z[Fgo$!?HQkhaVeQ9-tq$\\3\"Fjo7$$!?0@%ot%*y:j_5u1-'[Fgo$! ?TJB)4ep(R\"Hzm@*>5Fjo7$$!?v**)fReLMP\\(z&*yR[Fgo$!>^qI$G)y*fE_M7KO&*F jo7$$!?a;mkeMQ`8a'*yV>[Fgo$!>\"Qj.N,**48qY&4^)))Fjo7$$!?#)G:hWy8b?#))o .&)z%Fgo$!>[(Qrq-X:Sba5;D#)Fjo7$$!?F2H;lgUq\"os#[1!y%Fgo$!>6KjoLcL+bU& H:_wFjo7$$!?RcD-4OWx4ROqIfZFgo$!>\"zA%)RH:a&eEX1j,(Fjo7$$!?.7[#*pz=v+. 7SYQZFgo$!>\"*os])*\\UTE#G*e]X !*e3Wj+5z&Fjo7$$!?C)H>x3NShX#yx8+ZFgo$!>p4v#>)GX>7VU0qD&Fjo7$$!?3MOX\" eKI@&39&[%yYFgo$!>b]5EX#))QR;tQkJYFjo7$$!?OUpx5Vs*)eNi[2gYFgo$!>m*R\") )39-U*y\">1+6%Fjo7$$!?Wx4RcD-4OWP>qQYFgo$!>.F**H$[d<6Q>Fa7NFjo7$$!?RdH =t#4P[$RxKy>YFgo$!>_'z**GWltMy7^/=s)3l-*f%Fgo$!>T 7A7u)z(QfDzU)HCFjo7$$!?pw1F3LKHk=\">Nm^$3?![g<.>Fjo7$$!?@ &3MOX\"eKI@&3Q'eXFgo$!>%)QL3$y>Nhd%p(fi8Fjo7$$!?x2JC(*)eNUpxm*pRXFgo$! =@K5+6Ux*e^9!yT()Fjo7$$!?1E/XFgo$!=1+\"*=`rv#fL='*)eNFjo7$ $!?Unpy9fOY&=uW`!)\\%Fgo$\"=^\\kC1\"o&fj&)RPJb&))G:wD#p4Q)[-26 Fjo7$$!?A()[&>y7^/=sKC!RWFgo$\">ubXvrV&4#\\yEN`f\"Fjo7$$!?A!4OWx4RcD-< i)=WFgo$\">K4X(y%4yLCvHqX1#Fjo7$$!?iY'eMQ`8a;mCa$*R%Fgo$\">Ib-TZv1JKOV T1^#Fjo7$$!?Y$Q`8a;mkeM-%pxVFgo$\">\"[)y\\SZ0)4Bpb$o*HFjo7$$!?dH=t#4P[ $Rd\\8BeVFgo$\">.bV(Q9%G %oBc0[GEB'4%4\">3\\nuUFjo7$$!? 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