{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 0 0 128 0 1 0 2 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 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 } {PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Courier" 1 11 128 0 128 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Fo nt 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 11 0 128 128 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 " Kaffeeaufgabe (siehe Extre mwertaufgaben)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "Verkaufspreis:=2 0:\nVerkaufsmenge:=10000:\nPreissenkung:=0.02:\nAbsatzsteigerung:=100: \nSelbstkostenpreis:=14:\n\n" }{TEXT -1 15 " Gewinnfunktion" } {MPLTEXT 1 0 91 "\nf:=x->(Verkaufspreis-x*Preissenkung-Selbstkostenpre is)*(Verkaufsmenge+x*Absatzsteigerung);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*&,(%.VerkaufspreisG\" \"\"*&9$F/%-PreissenkungGF/!\"\"%2SelbstkostenpreisGF3F/,&%.Verkaufsme ngeGF/*&F1F/%1AbsatzsteigerungGF/F/F/F(F(F(" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 19 "1. erste Ableitung:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "f1:=unapply(diff(f(x),x),x);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#f1Gf*6#%\"xG6\"6$%)operatorG%&arrowGF(,&$\"&++%!\"#\"\"\"*&$\"$+%F/ F09$F0!\"\"F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 30 "2. Nullstellen: Bed. f(x) = 0" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 23 "nst:=\{solve(f(x)=0,x)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$nstG<$$!$+\"\"\"!$\"$+$F(" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "3. Scheitel:" }}{PARA 0 "" 0 "" {TEXT -1 29 " a) Bedingung: f ' (x) = 0" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "Scheitel_x:=solve(f1(x)=0,x);\nScheitel_y:=f(Sc heitel_x);\nPreis_pro_kg:=Verkaufspreis-Scheitel_x*Preissenkung;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%+Scheitel_xG$\"$+\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+Schei tel_yG$\"(+++)!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-Preis_pro_kgG $\"%+=!\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 " " }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "4. Grap h" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(f(x),x=0..360,0..80000); " }}{PARA 13 "" 1 "" {GLPLOT2D 418 418 418 {PLOTDATA 2 "6%-%'CURVESG6$ 7S7$$\"\"!F)$\"&++'F)7$$\"3A*******\\vp%y!#<$\"3r7m8!)zF27$$\"3o******\\03$y*F6$\"3yMU/>*e!* *zF27$$\"35+++$oUM0\"!#:$\"3yAvEfxG%*zF27$$\"3%****\\K7s;7\"F]p$\"3;tw %))y\"RqzF27$$\"34+++FN!G?\"F]p$\"3D?F()e9u'z(z&pF27$$\"3#*****\\xIA)z\"F]p$\"34fG4P) zcs'F27$$\"3!****\\K#Qfx=F]p$\"3E&*oyi\"e'fkF27$$\"3%)***\\2H'oY>F]p$ \"3]7?\"Q8qv?'F27$$\"3/++][!38-#F]p$\"3!QCQ,ufQ\"fF27$$\"3y*****fi*R)4 #F]p$\"3Y>h?Bl.(e&F27$$\"3#)****\\%p=Q<#F]p$\"39JY)[M*HW_F27$$\"3)**** \\7_!zYAF]p$\"3U2BC#zE5*[F27$$\"3$*****\\$H8yK#F]p$\"3An$4_rBQZ%F27$$ \"3*)*****z&eh+CF]p$\"3YZyjO/bwSF27$$\"3'******\\8[$yCF]p$\"30VS[$et*G OF27$$\"3%)***\\78&y[DF]p$\"3-UyVM#HD?$F27$$\"39+++t8zDEF]p$\"35[v&H#[ g8FF27$$\"3'****\\_C[#)p#F]p$\"3#Hf5]z0>B#F27$$\"3;++Dal)Rx#F]p$\"3'3U !o5M%fq\"F27$$\"3u*****\\fM![GF]p$\"3gujOri`p6F27$$\"30++DJgbDHF]p$\"3 km\\L5%zY%e!#97$$\"37+++)Q=-+$F]p$!392.k'Q*>ZRC?yHC'F]x7$$\"3?++DLAH_JF]p$!3[Zlh9Psk7F27$$\"3Q+++'yr=A$F]p$!3%GmX oYGM(=F27$$\"3.++]0yh,LF]p$!3ut#*=X!*)[f#F27$$\"31+++'fVHP$F]p$!3%\\#[ f>EshKF27$$\"3I++Dl<**[MF]p$!3sBY_K87&*RF27$$\"3>++vm&z<_$F]p$!3oPcbmV u=ZF27$$\"$g$F)$!3t++++++?bF2-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%+AXESLA BELSG6$Q\"x6\"Q!Ff[l-%%VIEWG6$;F(Fgz;F($\"&++)F)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 " Zylinderaufgabe, Oberfl\344che gegeben, Volumen \+ maximal" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }{MPLTEXT 1 0 137 " restart :\n gl:=2*Pi*r*h+Pi*r^2*2=150:\n a:=solve(gl,h);\n A:=r->Pi*r^2*a; \n \+ A1:=unapply(diff(A(r),r),r);\n rmin:= evalf(solve(A1(r)=0,r));\n\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG,$*(,&*&%#PiG\"\"\")%\"rG\"\"#F* F*\"#v!\"\"F*F)F/F,F/F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGf*6#% \"rG6\"6$%)operatorG%&arrowGF(*(%#PiG\"\"\")9$\"\"#F.%\"aGF.F(F(F(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1Gf*6#%\"rG6\"6$%)operatorG%&arrow GF(,&*(\"\"$\"\"\"%#PiGF/)9$\"\"#F/!\"\"\"#vF/F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%rminG6$$!+=z%4#G!\"*$\"+=z%4#GF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " " }}{PARA 0 "" 0 "" {TEXT -1 57 " Quader, doppelt so lang wie breit, Volumen gege ben" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 146 " V:=10.;\n gl:=aa*b*2*b=V: \n a:=solve(gl,aa):\n Ober:=b->2*a*b+4*b^2+4*a*b: \n Ober1:=unapply(di ff(Ober(b),b),b);\n L:= solve(Ober1(b)=0,b):\n\n b:=L[3];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VG$\"#5\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&Ober1Gf*6#%\"bG6\"6$%)operatorG%&arrowGF(,&*&$\"#I\"\"!\"\"\" 9$!\"#!\"\"*&\"\")F1F2F1F1F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"bG$\"+`ih`:!\"*" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "a:=evalf(solve( a1*b*2*b=V,a1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG$\"+P$)[r?!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalf(2*b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+1DB2J!\"*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 " minimale Entfernung (Ursprung/Punkt auf der Parabel) " }{MPLTEXT 1 0 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f: =x->x^2-2*x+2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "d:=x->sqr t(x^2+(f(x))^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dGf*6#%\"xG6\" 6$%)operatorG%&arrowGF(-%%sqrtG6#,&*$)9$\"\"#\"\"\"F4*$)-%\"fG6#F2F3F4 F4F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "d1:=unapply(dif f( d(x),x),x);\nxmin:= fsolve(d1(x)=0,x);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#d1Gf*6#%\"xG6\"6$%)operatorG%&arrowGF(,$*&#\"\"\"\" \"#F/*&,,*&\"\"*F/)9$F0F/F/*$)F6\"\"%F/F/*&F9F/)F6\"\"$F/!\"\"*&\"\")F /F6F/F=F9F/#F=F0,**&\"#=F/F6F/F/*&F9F/F;F/F/*&\"#7F/F5F/F=F?F=F/F/F/F( F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%xminG$\"+0f\"4(o!#5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "d(xmin);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+v_=&H\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "\n\n" }}{PARA 0 "" 0 "" {TEXT -1 82 " Laufbahn, Umfang gege ben, innenliegendes Rechteck mit maximalem Fl\344cheninhalt" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 137 "restart: Laenge:=500.: gl:= 2*Pi*r+2*aa=Laenge:\n a:=solve(gl,aa);\n A:=r->a*2*r; \n A1:=unapply(d iff(A(r),r),r);\n rmin:= solve(A1(r)=0,r);\n\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG,&*&$\"+aEfTJ!\"*\"\"\"%\"rGF*!\"\"$\"$]#\"\"!F* " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGf*6#%\"rG6\"6$%)operatorG%&a rrowGF(,$*(\"\"#\"\"\"%\"aGF/9$F/F/F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1Gf*6#%\"rG6\"6$%)operatorG%&arrowGF(,&*&$\"+iqjc7! \")\"\"\"9$F1!\"\"$\"$+&\"\"!F1F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%rminG$\"+wN()yR!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "a:=solve(2*Pi*rmin+2*x=Laenge,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG$\"++++]7!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 " Kabelverlegung (Land/Wasse r, unterschiedliche Kosten)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "restart: \nk:=x->x*700.+ sqrt( (10-x)^2+ 16)*900;\nk1:=unapply(d iff(k(x),x),x);\nxmin:= solve(k1(x)=0,x);\n\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"kGf*6#%\"xG6\"6$%)operatorG%&arrowGF(,&*&$\"$+(\"\" !\"\"\"9$F1F1*&\"$+*F1-%%sqrtG6#,&*$),&\"#5F1F2!\"\"\"\"#F1F1\"#;F1F1F 1F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k1Gf*6#%\"xG6\"6$%)opera torG%&arrowGF(,&$\"$+(\"\"!\"\"\"*(\"$]%F0,(\"$;\"F0*&\"#?F09$F0!\"\"* $)F7\"\"#F0F0#F8F;,&F6F8*&F;F0F7F0F0F0F0F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%xminG$\"+KDD]]!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalf(k(xmin));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"++ " 0 "" {MPLTEXT 1 0 4 "\n\n\n\n" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 " minimale Entfernung eines P unkts A(x0/y0) zu einem Punkt auf einem Graphen" }}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "f:=x->1/ x^2:\nx0:=3:\ny0:=2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "d:= x->sqrt((x-x0)^2+(f(x)-y0)^2);\nplot(d(x),x=1..4,y=0..6);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dGf*6#%\"xG6\"6$%)operatorG %&arrowGF(-%%sqrtG6#,&*$),&9$\"\"\"%#x0G!\"\"\"\"#F4F4*$),&-%\"fG6#F3F 4%#y0GF6F7F4F4F(F(F(" }}{PARA 13 "" 1 "" {GLPLOT2D 459 459 459 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$\"\"\"\"\"!$\"3\")*y*\\xz1OA!#<7$$\"31 ++]i9Rl5F-$\"30#)zA\"4:\\B#F-7$$\"34+]PC#)GA6F-$\"3?r'[\"QNnJAF-7$$\"3 %****\\Peui=\"F-$\"3Ipc#\\0R`A#F-7$$\"33++D'3&o]7F-$\"3$olia=:i@#F-7$$ \"3/+](oX*y98F-$\"3^2IF(o*o/AF-7$$\"3#***\\P9CAu8F-$\"31M^3vR8#>#F-7$$ \"3.+]P*zhdV\"F-$\"3gZMFJfbx@F-7$$\"3++]P>fS*\\\"F-$\"3QS'fb0?6;#F-7$$ \"35+](=$f%Gc\"F-$\"3^9k_Y#zO9#F-7$$\"3$*****\\#y,\"G;F-$\"3\"4QXwAZ\\ 7#F-7$$\"37++Dr\"zbo\"F-$\"35#*R2LA,3@F-7$$\"3%*****\\(4&G]vIQDp?F-7$$\"3%*****\\-*oy(=F-$\"3%Rp A9F!o]?F-7$$\"35+]PpnsM>F-$\"3iz1(GQ+T.#F-7$$\"3,++]siL-?F-$\"3?C&*H!) G\"\\,#F-7$$\"3-+++!R5'f?F-$\"3_()HW()zB**>F-7$$\"3)***\\P/QBE@F-$\"3w _6u9)>=)>F-7$$\"3!******\\\"o?&=#F-$\"3Ke$y'>%\\s'>F-7$$\"3%)**\\Pa&4* \\AF-$\"3qsI]=&*H_>F-7$$\"3&)**\\7j=_6BF-$\"3dA6[4kF-7$$\"33++vVy!e P#F-$\"3oLE/KWuE>F-7$$\"3K+](=WU[V#F-$\"3+.%QnpWl\">F-7$$\"3)****\\7B> &)\\#F-$\"3RK\"RvuIp!>F-7$$\"3)***\\P>:mkDF-$\"3G))ed==b)*=F-7$$\"3'** *\\iv&QAi#F-$\"3)p4!>-?l#*=F-7$$\"31++vtLU%o#F-$\"3W;^+CJz()=F-7$$\"37 +++bjm[FF-$\"3YIX73dZ%)=F-7$$\"3\"****\\(yb^6GF-$\"3as@@f\"\\H)=F-7$$ \"3)***\\PMaKsGF-$\"3!=Dv5rCJ)=F-7$$\"3=++D6W%)RHF-$\"3O0=z)>b_)=F-7$$ \"3z*****\\@80+$F-$\"3m\\7ykp#*))=F-7$$\"31++]7,HlIF-$\"3o!e<].(p%*=F- 7$$\"3()**\\P4w)R7$F-$\"3!4k#oq+e,>F-7$$\"3;++]x%f\")=$F-$\"3TI`htK!4 \">F-7$$\"3!)**\\P/-a[KF-$\"3uE+(*)3$Q@>F-7$$\"3/+](=Yb;J$F-$\"3J!))e9 w#4M>F-7$$\"3')****\\i@OtLF-$\"3Y#Q[^qL#[>F-7$$\"3')**\\PfL'zV$F-$\"3/ 'pdB$z#['>F-7$$\"3>+++!*>=+NF-$\"3Sn&en\\5D)>F-7$$\"3-++DE&4Qc$F-$\"3 \\F(R]B$G-?F-7$$\"3=+]P%>5pi$F-$\"3gb9'fcSN-#F-7$$\"39+++bJ*[o$F-$\"3* >Y(H+Z[W?F-7$$\"33++Dr\"[8v$F-$\"3O0ipBZ5q?F-7$$\"3++++Ijy5QF-$\"3#4; \"Q#zQW4#F-7$$\"31+]P/)fT(QF-$\"3sN!oz#G\"=7#F-7$$\"31+]i0j\"[$RF-$\"3 C=Nd/\"\\$\\@F-7$$\"\"%F*$\"3=^S\"GWX.=#F--%'COLOURG6&%$RGBG$\"#5!\"\" $F*F*F_[l-%+AXESLABELSG6$Q\"x6\"Q\"yFd[l-%%VIEWG6$;F(Fdz;F_[l$\"\"'F* " 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }} }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "d1:=unapply(diff( d(x),x), x):\nxmin:= fsolve(d1(x)=0,x);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%xminG$\"+s^WNG!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "d(xmin);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+tE#G)= !\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "33 0 0 " 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }