{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 1 24 0 255 0 1 0 0 1 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 -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 }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 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE " " -1 -1 "" 0 1 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 "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 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 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 102 "Alexander Rabe und Mich ael Dorsch Klasse 11d Isolde-Kurz-Gymnasium Reutlingen 2 8.03.2000" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 257 "" 0 "" {TEXT 256 27 "Untersuchen des Vorzeichens" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 176 "Zu einer Funktion werden Kandidaten f\374r Extrema berec hnet und mit Hilfe des Vorzeichens geschaut, ob es sich um einen Hochp unkt, einen Tiefpunkt, oder einen Wendepunkt handelt." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Parab elfunktion:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "#f:=x->a*x^4 +b*x^3+c*x^2+d*x+e;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Wertedefin ition:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "#(a:=2; b:=5; c:= -1; d:=0; e:=5;)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Kontrollausga be der eingesetzten Parabelfunktion:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f:=x->(x-2)^4-(x-2)^2-3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&arrowGF(,(*$),&9$\"\"\" !\"#F1\"\"%\"\"\"F1*$)F/\"\"#F4!\"\"!\"$F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$) ,&%\"xG\"\"\"!\"#F(\"\"%\"\"\"F(*$)F&\"\"#F+!\"\"!\"$F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot(f(x),x=0..3.7);" }}{PARA 13 " " 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Nullstelle n der Parabel:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "nf:=\{fso lve(f(x))\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#nfG<$$\"+k35D[!#5$ \"+9**[ " 0 "" {MPLTEXT 1 0 9 "af:=D(f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#afGR6#%\"xG6\"6$%)operatorG%&arrowGF(,(*$ ),&9$\"\"\"!\"#F1\"\"$\"\"\"\"\"%F0F2F5F1F(F(F(" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 6 "af(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$) ,&%\"xG\"\"\"!\"#F(\"\"$\"\"\"\"\"%F'F)F,F(" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 26 "Nullstellen der Ableitung:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 19 "na:=\{solve(af(x))\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#naG<%\"\"#,&F&\"\"\"*$-%%sqrtG6#F&\"\"\"#!\"\"F&,&F&F(F)#F(F& " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "Berechnung der Kandidaten f \374r Extrema, ausgedr\374ckt als Punkte:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 38 "kex:=\{[na[i],f(na[i])]$i=1..nops(na)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$kexG<%7$\"\"#!\"$7$,&F'\"\"\"*$-%%sqrtG6# F'\"\"\"#!\"\"F'#!#8\"\"%7$,&F'F+F,#F+F'F3" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "Bilden der zweiten Ableitung:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 11 "aaf:=D(af);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$a afGR6#%\"xG6\"6$%)operatorG%&arrowGF(,&*$),&9$\"\"\"!\"#F1\"\"#\"\"\" \"#7F2F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "aaf(x);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$),&%\"xG\"\"\"!\"#F(\"\"#\"\"\"\" #7F)F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Nullstellen der zweiten Ableitung:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "naa:=\{solve (aaf(x))\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$naaG<$,&\"\"#\"\"\"* $-%%sqrtG6#\"\"'\"\"\"#F(F-,&F'F(F)#!\"\"F-" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 51 "Kandidaten f\374r Wendepunkte, als Punkte ausgedr\374ck t:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "kwp:=\{[naa[i],f(naa[ i])]$i=1..nops(naa)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$kwpG<$7$, &\"\"#\"\"\"*$-%%sqrtG6#\"\"'\"\"\"#F)F.#!$8\"\"#O7$,&F(F)F*#!\"\"F.F1 " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Zeichnen der Parabel:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "p1:=plot([f],min(op(nf union na union naa))-1/2..max(op(nf union na union naa))+1/2): p1;" }} {PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Kontrollausgabe der Able itung:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "af(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$),&%\"xG\"\"\"!\"#F(\"\"$\"\"\"\"\"%F'F) F,F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Untersuchung des Vorzeich ens der Ableitung:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Der erste K andidat f\374r ein Extremum:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "limit(signum(af(x)),x=na[1],left);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "limit(signu m(af(x)),x=na[1],right);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "Folgerung: Da die Geschwindigkeit / das Vorzeichen von + nach - wechselt, handelt es sich um ein Maxim um." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "Der zweite Kandidat f\374r ein Extremum:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "limit(sig num(af(x)),x=na[2],left);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "limit(signum(af(x)),x=na[2] ,right);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "Folgerung: Da die Geschwindigkeit / das Vorzeich en von - nach + wechselt, handelt es sich um ein Minimum." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "Der dritte Kandidat f\374r ein Extremum: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "limit(signum(af(x)),x=n a[3],left);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "limit(signum(af(x)),x=na[3],right);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "Folgerung: Da die Geschwindigkeit / das Vorzeichen von \+ - nach + wechselt, handelt es sich um ein Minimum." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Zeichnung der Ableitung:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "p2:=plot(af(x),x=1..3,color=blue): p2;" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Ableitung und Funktion in ein em Schaubild:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "plot(\{f(x ),af(x)\},x=-0.5..4,y=-4..2,color=[red,blue]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 " alexander.rabe@ikg.rt.bw.schule.de oder \+ 0179 2105529 (Handy)" }}{PARA 0 "" 0 "" {TEXT -1 102 " michael.dorsch@ ikg.rt.bw.schule.de oder michael.dorsch@gmx.de oder 07121/46292 oder F ax 2384749465986" }{MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 94 }{VIEWOPTS 1 1 0 1 1 1803 }