{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 18 0 0 0 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 -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 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "H eading 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 -1 8 2 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 "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 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 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 84 " Frieder Weiblen, Sebastia n Pater, Joachim Reichel, Isolde-Kurz-Gymnasium, 28.3.2000" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 256 "" 0 "" {TEXT -1 1 " " }{TEXT 256 16 "Kurvendiskussion" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 "Aufgabe Nr. 1" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 26 "f:=x->2*x ^4-2*x^3-5*x^2-2;" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "f:=x->2 *x^4-2*x^3-5*x^2-2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6 \"6$%)operatorG%&arrowGF(,**$)9$\"\"%\"\"\"\"\"#*$)F/\"\"$F1!\"#*$)F/F 2F1!\"&F6\"\"\"F(F(F(" }}}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Schaubild:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "p1:=plot(f(x),x=-1.5..2.5,y=-12..5,thickness=2): p1; " }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$ 7in7$$!1+++++++:!#:$\"1++++++DOF*7$$!1LLL$Q6GT\"F*$\"1D\"3'>U=G;F*7$$! 1nm;M!\\pL\"F*$\"1m5STv!3K#!#;7$$!1LLL))Qj^7F*$!1Tnm9r&H+\"F*7$$!1LLL= Kvl6F*$!1QQQNXxK>F*7$$!1nm;C2G!3\"F*$!1'[z#3]$)*e#F*7$$!1LL$3yO5+\"F*$ !1&RJ;*)Qe*HF*7$$!1,++vE%)*=*F7$!1j\"=59oRC$F*7$$!1MLL3WDT$)F7$!1YHh#p O*\\LF*7$$!1,++vvQ&\\(F7$!1,fDR-fNLF*7$$!1mmmm&4`i'F7$!1d;3EYvFKF*7$$! 1LLL$QW*eeF7$!1^CzvqWyIF*7$$!1,+++()>'*\\F7$!172$3`\\S(GF*7$$!1++++0\" *HTF7$!1_JVyYu`EF*7$$!1++++83&H$F7$!1*[_DiZxW#F*7$$!1LLL3k(p`#F7$!1rVd y,(3G#F*7$$!1nmmmj^N;F7$!1cz(f#\\cB@F*7$$!1!ommm9'=()!#<$!1U))yzgcO?F* 7$$\"1+*****\\s]k\"!#=$!1.q?SN,+?F*7$$\"19LLL`dF!)F[q$!16j*HbsJ.#F*7$$ \"1,++D2Yl;F7$!1kb#yR)QY@F*7$$\"1+++v\"ep[#F7$!1w\"[#y2OKBF*7$$\"1MLL$ e/TM$F7$!1=y2(>M*3EF*7$$\"1LLLeDBJTF7$!1K&o_B8h$HF*7$$\"1mmm;kD!)\\F7$ !1uG)\\`gTO$F*7$$\"1jmm\"f`@'eF7$!1g&o=sd\\)QF*7$$\"1)****\\nZ)HmF7$!1 R3jJg;%R%F*7$$\"1lmm;$y*euF7$!1BTY*yJIT?>jF*7$$\"1(****\\7RV'**F7$!1ycza )e9(pF*7$$\"1+++:#fk3\"F*$!1***R'p*3-o(F*7$$\"1LLL`4Nn6F*$!1(=ppC66G)F *7$$\"1+++],s`7F*$!1!>h#G:5f))F*7$$\"1mm;zM)>L\"F*$!1:t'paF=I*F*7$$\"1 +++qfa<9F*$!1=,T9'\\%o'*F*7$$\"1mm\"zy*zd9F*$!19v27PH*y*F*7$$\"1LL$eg` !)\\\"F*$!1%>1EBJ?()*F*7$$\"1mm;W/8S:F*$!1\")pB9$3O\"**F*7$$\"1++]#G2A e\"F*$!1_R&z\\4[!**F*7$$\"1mm\"H3XLi\"F*$!1S?OOo+V)*F*7$$\"1LLL$)G[k;F *$!1n%3r:]Ss*F*7$$\"1mm\"zM]vq\"F*$!149ViX?L&*F*7$$\"1++]7yh]F*$!1_skJ%4HV( F*7$$\"1LL$e#pa-?F*$!1p7=g,')[fF*7$$\"1nm\"HB-7/#F*$!1/XI\"*RMA^F*7$$ \"1+++Sv&)z?F*$!1Vn^fS%z>%F*7$$\"1nm;%)3;C@F*$!1>Gtmlh6IF*7$$\"1LLLGUY o@F*$!1-j=4QQ#o\"F*7$$\"1++]n'*33AF*$!1#)*o$)p#ofOF77$$\"1nmm1^rZAF*$ \"16XN:d)o2\"F*7$$\"1LLe*3k**G#F*$\"19=.]R>hFF*7$$\"1++]sI@KBF*$\"1t&> \\-iKg%F*7$$\"1+++S2lsBF*$\"1XDhKA+@lF*7$$\"1++]2%)38CF*$\"1uX3(*>x'f) F*7$$\"1+]i0j\"[V#F*$\"1h-O+-wz(*F*7$$\"1++v.UacCF*$\"1,B&*309,6!#97$$ \"1+](=5s#yCF*$\"1$ojexy#H7F\\^l7$$\"1+++++++DF*$\"1+++++]i8F\\^l-%'CO LOURG6&%$RGBG$\"#5!\"\"\"\"!F^_l-%+AXESLABELSG6$Q\"x6\"Q\"yFc_l-%*THIC KNESSG6#\"\"#-%%VIEWG6$;$F*F]_l$\"#DF]_l;$!#7F^_l$\"\"&F^_l" 1 2 0 1 2 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Berechnung der Nullstellen der Funktion:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "nullf:=\{fsolve(f(x))\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&nullfG<$$!+qZbA8!\"*$\"+GG[=AF(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "`Nullstellen der Funktion:`; [nullf[i],f(nullf[i])]$i=1..nops(nullf);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Nullstellen~der~Funktion:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$ 7$$!+qZbA8!\"*$!#5F&7$$\"+GG[=AF&$\"\"\"!\")" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 38 "Zeichnen der Nullstellen der Funktion:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "p2:=plot([[nullf[i],f(nullf[i])]$i= 1..nops(nullf)],style=point,symbol=diamond,color=black):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Bilden der Ableitung:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "af:=D(f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%#afGR6#%\"xG6\"6$%)operatorG%&arrowGF(,(*$)9$\"\"$\"\"\"\"\")*$)F/ \"\"#F1!\"'F/!#5F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "Zeichne n der Ableitung:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "p3:=plo t(af(x),x=-1.5..2.5,y=-12..5,color=blue): p3;" }}{PARA 13 "" 0 "" {TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6& -%'CURVESG6#7U7$$!1+++++++:!#:$!1++++++]D!#97$$!1LLL$Q6GT\"F*$!1&Hy48G 3/#F-7$$!1nm;M!\\pL\"F*$!10(ymvvsk\"F-7$$!1LLL))Qj^7F*$!1FSVRO&pD\"F-7 $$!1LLL=Kvl6F*$!1SzBh*Q-<*F*7$$!1nm;C2G!3\"F*$!1%oJ#Rzy%G'F*7$$!1LL$3y O5+\"F*$!1kr,e&))p-%F*7$$!1,++vE%)*=*!#;$!1u#F*7$$!1,+++()>'*\\FO$\"1A2Yfwv+DF* 7$$!1++++0\"*HTFO$\"1:m9KL\"F*$!1b]R^s[f]F*7$$\"1+++qfa<9F*$!18n3)QHVW$F*7$$\"1LL$eg`!)\\\"F *$!1?j\"Ql#\\]:F*7$$\"1++]#G2Ae\"F*$\"1R;IH%\\dW)FO7$$\"1LLL$)G[k;F*$ \"1:?w2PzBOF*7$$\"1++]7yh]F*$\"1y;$*G:o@:F-7$$\"1LL$e#pa-?F*$\"1\"*[2)>=e,# F-7$$\"1+++Sv&)z?F*$\"1vq#e^3B_#F-7$$\"1LLLGUYo@F*$\"1H+6y)*\\nJF-7$$ \"1nmm1^rZAF*$\"1%[I8q " 0 "" {MPLTEXT 1 0 22 "nulla :=\{solve(af(x))\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&nullaG<%\"\" !,&#\"\"$\"\")\"\"\"*$-%%sqrtG6#\"#*)\"\"\"#F+F*,&F(F+F,#!\"\"F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "[nulla[i],af(nulla[i])]$i=1. .nops(nulla);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6%7$\"\"!F$7$,&#\"\"$\" \")\"\"\"*$-%%sqrtG6#\"#*)\"\"\"#F*F),**$)F&F(F0F)*$)F&\"\"#F0!\"'#!#: \"\"%F*F+#!\"&F;7$,&F'F*F+#!\"\"F),**$)F?F(F0F)*$)F?F7F0F8F9F*F+#\"\"& F;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Zeichnung der Nullstellen d er Ableitung:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "p4:=plot([ [nulla[i],af(nulla[i])]$i=1..nops(nulla)],style=point,symbol=diamond,c olor=black):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Berechnung der Ka ndidaten f\374r Extrema:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 " `Kandidaten f\374r Extrema:`; [nulla[i],f(nulla[i])]$i=1..nops(nulla );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%8Kandidaten~f|gzr~Extrema:G" }} {PARA 12 "" 1 "" {XPPMATH 20 "6%7$\"\"!!\"#7$,&#\"\"$\"\")\"\"\"*$-%%s qrtG6#\"#*)\"\"\"#F+F*,**$)F'\"\"%F1\"\"#*$)F'F)F1F%*$)F'F7F1!\"&F%F+7 $,&F(F+F,#!\"\"F*,**$)F>F6F1F7*$)F>F)F1F%*$)F>F7F1F " 0 "" {MPLTEXT 1 0 89 "p5:=plot([[nulla[i],f(n ulla[i])]$i=1..nops(nulla)],style=point,symbol=circle,color=blue):" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "Untersuchung des Vorzeichens zur \+ Unterscheidung von Extrema und Wendepunkt:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Der erste Punkt:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "limit(signum(af(x)),x=nulla[1],left);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "li mit(signum(af(x)),x=nulla[1],right);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 98 "Folgerung: es handelt \+ sich um ein Maximum, da die Steigung / das Vorzeichen von + nach - wec hselt." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Der zweite Punkt:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "limit(signum(af(x)),x=nulla[ 2],left);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "limit(signum(af(x)),x=nulla[2],right);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "Folgerung: Es handelt sich um ein Minimum, da das Vorzeic hen von - nach + wechselt." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "limit(signum(af(x)),x=nulla[3],left);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "lim it(signum(af(x)),x=nulla[3],right);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "Folgerung: Minimum, da das Vorzeichen von - nach + wechselt." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Zweite Ableit ung :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "aaf:=(D(af));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$aafGR6#%\"xG6\"6$%)operatorG%&arrow GF(,(*$)9$\"\"#\"\"\"\"#CF/!#7!#5\"\"\"F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Zeichnen der zweiten Ableitung:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 53 "p6:=plot(aaf(x),x=-1.5..2.5,y=-12..5,color=nav y): p6;" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CU RVESG6#7S7$$!1+++++++:!#:$\"#i\"\"!7$$!1LLL$Q6GT\"F*$\"1$*Hqr+'e[&!#97 $$!1nm;M!\\pL\"F*$\"1Q?!*ot<%*[F37$$!1LLL))Qj^7F*$\"11'=ISq'*\\FP$\"14;(zy= j)>F*7$$!1++++0\"*HTFP$!1/axG#)G1&*FP7$$!1++++83&H$FP$!1uOLay3SMF*7$$! 1LLL3k(p`#FP$!1BW&)y%G4T&F*7$$!1nmmmj^N;FP$!16xW^5S&R(F*7$$!1!ommm9'=( )!#<$!1Ug!*f?Lr()F*7$$\"1+*****\\s]k\"!#=$!1Fv'>fn>+\"F37$$\"19LLL`dF! )F]q$!1QUAK['33\"F37$$\"1,++D2Yl;FP$!1zNwg]GL6F37$$\"1+++v\"ep[#FP$!1; #fy\"f**\\6F37$$\"1MLL$e/TM$FP$!1'\\d))p**G8\"F37$$\"1LLLeDBJTFP$!1*>v \"Gz8'3\"F37$$\"1mmm;kD!)\\FP$!17?eu)fB+\"F37$$\"1jmm\"f`@'eFP$!14.Du: -(y)F*7$$\"1)****\\nZ)HmFP$!128^jfk1uF*7$$\"1lmm;$y*euFP$!1m\"fJ<[!)f& F*7$$\"1*******R^bJ)FP$!1N*\\$fo/$Q$F*7$$\"1'*****\\5a`\"*FP$!1weJ!fRH v)FP7$$\"1(****\\7RV'**FP$\"1v8_dg#>(=F*7$$\"1+++:#fk3\"F*$\"1!)>gSk$> H&F*7$$\"1LLL`4Nn6F*$\"1/y&z^'y'p)F*7$$\"1+++],s`7F*$\"1`%Q[$**)yE\"F3 7$$\"1mm;zM)>L\"F*$\"1]]0)z^'f;F37$$\"1+++qfa<9F*$\"1y<&4i#f@@F37$$\"1 LL$eg`!)\\\"F*$\"1-1GF2L)e#F37$$\"1++]#G2Ae\"F*$\"1#[5X)HY4JF37$$\"1LL L$)G[k;F*$\"1^JQ&QG=l$F37$$\"1++]7yh]F*$\"1(R)RjAkIbF37$$\"1LL$e#pa-?F*$\"1! )[RX(49A'F37$$\"1+++Sv&)z?F*$\"1Vw1!o3h)oF37$$\"1LLLGUYo@F*$\"1pq%*))> @$o(F37$$\"1nmm1^rZAF*$\"10,x`v2G%)F37$$\"1++]sI@KBF*$\"1QdHqqYb#*F37$ $\"1++]2%)38CF*$\"18'y+N[z+\"!#87$$\"1+++++++DF*$\"$5\"F--%+AXESLABELS G6$Q\"x6\"Q\"yFa[l-%'COLOURG6&%$RGBG$\")!\\DP\"!\")Fg[l$\")viobFi[l-%% VIEWG6$;$F*!\"\"$\"#DFa\\l;$!#7F-$\"\"&F-" 1 2 0 1 0 2 6 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Nullstelle der zweiten Ableitung:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "nullaa:=\{solve(aaf(x))\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'nullaaG<$,&#\"\"\"\"\"%F(*$-%%sqrtG6#\"#p\"\"\"#F(\" #7,&F'F(F*#!\"\"F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "[null aa[i],aaf(nullaa[i])]$i=1..nops(nullaa);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$7$,&#\"\"\"\"\"%F&*$-%%sqrtG6#\"#p\"\"\"#!\"\"\"#7,(*$)F$\"\"#F- \"#C!#8F&F(F&7$,&F%F&F(#F&F0,(*$)F8F4F-F5F6F&F(F/" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 47 "Zeichnung der Nullstelle der zweiten Ableitung:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "p7:=plot([[nullaa[i],aaf(n ullaa[i])]$i=1..nops(nullaa)],style=point,symbol=diamond,color=black): " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Berechnung der Wendepunkte de r Funktion:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "`Wendepunkt` ;[nullaa[i],f(nullaa[i])]$i=1..nops(nullaa);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%+WendepunktG" }}{PARA 12 "" 1 "" {XPPMATH 20 "6$7$,&# \"\"\"\"\"%F&*$-%%sqrtG6#\"#p\"\"\"#!\"\"\"#7,**$)F$F'F-\"\"#*$)F$\"\" $F-!\"#*$)F$F4F-!\"&F8F&7$,&F%F&F(#F&F0,**$)F=F'F-F4*$)F=F7F-F8*$)F=F4 F-F;F8F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Zeichnung der Wendepu nkte:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "p8:=plot([[nullaa[ i],f(nullaa[i])]$i=1..nops(nullaa)],style=point,symbol=cross,color=nav y):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "Bilden der dritten Ableitu ng:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "aaaf:=D(aaf);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%aaafGR6#%\"xG6\"6$%)operatorG%&arro wGF(,&9$\"#[!#7\"\"\"F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Ze ichnung der dritten Ableitung:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "p9:=plot(aaaf(x),x=-1.5..2.5,y=-12..5,color=gray): p9;" }} {PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "Funktion, Ableitung, Nul lstellen und Extrema / Wendepunkt in einem Schaubild:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "with(plots): display(p1,p2,p3,p4,p5 ,p6,p7,p8,p9);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Unters uchung des Verhaltens f\374r gro\337e und kleine x:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Kontrollausgabe:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%\"xG\" \"%\"\"\"\"\"\"*$)F&\"\"$F(!\"&*$)F&\"\"#F(\"\"'F&F'!\"%F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "F\374r gro\337e x ist die gr\366\337te Ho chzahl ma\337geblich verantwortlich:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "gross:=select(has,expand(f(x)),x^degree(f(x),x));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&grossG*$)%\"xG\"\"%\"\"\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "F\374r kleine x ist der Rest der P arabelfunktion zu betrachten:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "klein:=f(x)-gross;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&kleinG, **$)%\"xG\"\"$\"\"\"!\"&*$)F(\"\"#F*\"\"'F(\"\"%!\"%\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 143 "Nun wird f\374r die gr\366\337te Hochzah l der Vorfaktor ver\344ndert, bis er den urspr\374nglichen Wert hat; d er Vorfaktor n\344hert sich seinem Originalwert an:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s1:=seq(i*gross/10,i=0..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#s1G6-\"\"!,$*$)%\"xG\"\"%\"\"\"#\"\"\"\"#5,$ F(#F.\"\"&,$F(#\"\"$F/,$F(#\"\"#F2,$F(#F.F8,$F(#F5F2,$F(#\"\"(F/,$F(#F +F2,$F(#\"\"*F/F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "Das gleiche \+ wird nun auch f\374r kleine x gemacht:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s2:=seq(i*klein/10,i=0..10);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#s2G6-\"\"!,**$)%\"xG\"\"$\"\"\"#!\"\"\"\"#*$)F*F/F,# F+\"\"&F*#F/F3#!\"#F3\"\"\",*F(F.F0#\"\"'F3F*#\"\"%F3#!\"%F3F7,*F(#!\" $F/F0#\"\"*F3F*F9#!\"'F3F7,*F(F6F0#\"#7F3F*#\"\")F3#!\")F3F7,*F(#!\"&F /F0F+F*F/F6F7,*F(FAF0#\"#=F3F*FG#!#7F3F7,*F(#!\"(F/F0#\"#@F3F*#\"#9F3# !#9F3F7,*F(F>F0#\"#CF3F*#\"#;F3#!#;F3F7,*F(#!\"*F/F0#\"#FF3F*FQ#!#=F3F 7,*F(FOF0F:F*FF7" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 99 "Die Ver \344nderung von gross (es \344ndert sich die \326ffnung) wird eingezei chnet als eine Folge von plots." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "display(seq(plot(s1[i],x=-2..2),i=1..11),insequence=true,view= [-1.5..1.5,-1..15]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 97 "Nun wird nur der f\374r die kleinen x verantwortliche Teil der \+ Parabelfunktion ver\344ndert gezeichnet." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "display(seq(plot(s2[i],x=-3.5..2.5),i=1..11),insequen ce=true,view=[-3.5..2.5,-20..20]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 63 "Zu dem original gross wird der Bereich des kleinen x ve r\344ndert:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "display(seq( plot(s1[11]+s2[i],x=-2..2.5),i=1..11),insequence=true);" }}{PARA 13 " " 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 185 "Die Ver\344nderung von gross (es \+ \344ndert sich die \326ffnung) wird eingezeichnet als eine Folge von p lots. Des weiteren wird zu dem original gross nun noch der Bereich des kleinen x ver\344ndert:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "display([seq(plot(s1[i],x=-2.5..2.5),i=1..11),seq(plot(s1[11]+s2[ i],x=-2..2.5),i=1..11)],insequence=true);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 267 "Zuerst wird der Bereich f\374r gro\337e x alle ine ver\344ndert gezeigt, danach kommt zu dem nun unver\344nderten Wer t f\374r gro\337e x noch eine Ver\344nderung des Bereiches f\374r klei ne x. Zum Schluss wird noch zu dem unver\344nderten Bereich des kleine n x der Bereich f\374r gro\337e x ver\344ndert." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 152 "display([seq(plot(s1[i],x=-2.5..2.5),i=1..11) ,seq(plot(s1[11]+s2[i],x=-2.5..2.5),i=1..11),seq(plot(s1[i]+s2[11],x=- 2.5..2.5),i=1..11)],insequence=true);" }}{PARA 13 "" 1 "" {TEXT -1 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 253 "Man kann das Verhalten der Parabelfunktion auch unt ersuchen, indem man sagt, dass f\374r einen bestimmten Bereich eine Fu nktion f\374r die kleinen x verantwortlich ist und au\337erhalb dieses Bereiches zeichnet eine andere Funktion das Verhalten f\374r gro\337e x auf." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "ff:=x-> if type( x,numeric) then if x>-1 and x<1 then 1 else 0 fi else 'ff'(x) fi;" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%#ffGR6#%\"xG6\"6$%)operatorG%&arrowG F(@%-%%typeG6$9$%(numericG@%32!\"\"F02F0\"\"\"F7\"\"!-.F$6#F0F(F(F(" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "g:=x-> if type(x,numeric) \+ then if x<-1 or x>1 then 1 else 0 fi else 'g'(x) fi;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"gGR6#%\"xG6\"6$%)operatorG%&arrowGF(@%-%%typeG6$ 9$%(numericG@%52F0!\"\"2\"\"\"F0F7\"\"!-.F$6#F0F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 138 "Rot (ff) zeichnet im Bereich von -1 bis 1 das Verhalten f\374 r kleine x auf, w\344hrend gr\374n (g) f\374r das Verhalten von kleine n x zust\344ndig ist." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "pl ot([ff,g],-2..2,color=[red,green],thickness=2);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 110 "Zun\344chst wird das Verhalten f\374r gr o\337e x alleine gezeigt, bis dann der Bereich f\374r kleine x (blau) \+ hinzukommt. " }}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 217 "display([seq(plot (((s1[i])*g(x)),x=-3..3,discont=true,color=red),i=1..11),seq(plot([(s1 [11]+s2[i])*g(x),(s1[11]+s2[i])*ff(x)],x=-3..3,discont=true,color=[red ,blue]),i=1..11)],insequence=true,view=[-2.5..2.5,-10..5]); " }}}}} {MARK "0 0 0" 52 }{VIEWOPTS 1 1 0 1 1 1803 }