{VERSION 2 3 "IBM INTEL NT" "2.3" } {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 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 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 "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 6 6 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 "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 6 "Quelle" }}{PARA 0 "" 0 "" {TEXT -1 344 "Dateiname: ableitun.mws\nDateigr\366\337e: 4 KB\nName : Annika Possekel\nSchule: Isolde-Kurz-Gymnasium, 72764 Reutlingen \nK lasse: 11d\nDatum: 20.02.97\nFach: Mathematik\nThema: Differenzialrech nung\nStichw\366rter: Funktion mit 1. und 2. Ableitung\nKurzbeschreibu ng: Allgemein Ableitung von Funktionen\nBeispiel: Funktion mit 1. und \+ 2. Ableitung und Darstellung \n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 10 "Allgemein:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Funktion:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "x->x^n+y;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#:6#%\"xG6\"6$%)operatorG%&arrowGF&,&)9$%\"nG\"\"\"%\" yGF.F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "Ableitung der Funktio n:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "x->n*x^(n-1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#:6#%\"xG6\"6$%)operatorG%&arrowGF&*&% \"nG\"\"\")9$,&F+F,!\"\"F,F,F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 256 "" 0 "" {TEXT -1 9 "Beispiel:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 21 "restart: with(plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Bestimmung der Funktion:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f:=x->2*x^3-4*x^2+3*x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG:6#%\"xG6\"6$%)operatorG%&arrowGF(,(*$9$\"\"$\"\"#*$F.F0! \"%F.F/F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Darstellung der Fu nktion in einem Plot." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "A: =plot(f(x),x=-2..3,-10..10,color=black):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "1.Ableitung d er Funktion f(x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "d1:=di ff(f(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#d1G,(*$%\"xG\"\"#\" \"'F'!\")\"\"$\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Darstellu ng der 1.Ableitung in einem Plot:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "B:=plot(d1,x=-2..3,-10..10,color=green):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "2.Ableitung der Funktion f(x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "d2:=diff(d1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% #d2G,&%\"xG\"#7!\")\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Dars tellung der 2.Ableitung in einem Plot:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "C:=plot(d2,x=-2..3,-10..10,color=blue):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 93 "Darstellung der Funktion f(x), der 1.Ableitung und der 2.Ableit ung in einem gemeinsamen Plot:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "display(A,B,C);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 14 "Beobachtungen:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "- Die Extrema einer Funktion entsprechen den Nullstellen der Ablei tung der Funktion." }}{PARA 0 "" 0 "" {TEXT -1 84 "- Die Wendepunkte e iner Funktion entsprechen den Extrema der Ableitung der Funktion." }} {PARA 0 "" 0 "" {TEXT -1 91 "- Die Wendepunkte einer Funktion entsprec hen den Nullstellen der 2. Ableitung der Funktion." }}}}{MARK "1" 0 } {VIEWOPTS 1 1 0 1 1 1803 }