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Wachstumsge schwindigkeit an einer Stelle [cm/Tag]" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(f(4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+JXOl@!\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "2. momentane \304nderungsrate der Wachstumsgeschwindig keit zu Beginn. [cm/Tag pro Tag]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " f1:=unapply(diff(f(x),x),x);\nf1(0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1Gf*6#%\"xG6\"6$%)operatorG%&arrowGF(,&*&\"#S \"\"\"-%$expG6#,$*&#F/\"\"#F/9$F/!\"\"F/F/*(\"#?F/F7F/F0F/F8F(F(F(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"#S" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "3. durchschnittliche \304nderungsrate der Wachstumsgeschwind igkeit im Intervall [0; 1]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 " evalf((f(1)-f(0))/(1-0));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# $\"+RE7EC!\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "4. Zeitpunkt \+ mit der gr\366\337ten Wachstumsgeschwindigkeit " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "T1:=fsolve( f1(x)=0,x);\ndiv(T1*24,24); # T age, Stunden" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#T1G$\"\"#\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$$\"+++++?!\"*$\"\"!F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "5. Zeitpunkte mit der Wachstumsgeschwi ndigkeit 10 cm/Tag" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " fsol ve( f(x)=10,x=0..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+jqU))G!#5 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "fsolve( f(x)=10,x=2..10 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+p8PBl!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 " \+ 6. Zeitpunkt, f\374r den die \304nderung der Wachstumsgeschwindigkei t am kleinsten ist." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 " f2:=unapply(diff(f1(x),x),x );\nfsolve( f2(x)=0,x=2..10);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# f2Gf*6#%\"xG6\"6$%)operatorG%&arrowGF(,&*&\"#S\"\"\"-%$expG6#,$*&#F/\" \"#F/9$F/!\"\"F/F8*(\"#5F/F7F/F0F/F/F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"%\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 " 7. H\366he der Pflanze nach 6 Stunden " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " ta:=6/24; # in Tagen\n evalf(int(f(x),x=0..ta)+f0); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#taG#\"\"\"\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\")vb]J!\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 " 8. Zeitpunkt, f\374r den die Pflanze 100 cm hoch ist." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 " T2:= fsolve(int(f(x),x=0..t )+f0=100,t=0..10);\n div(T2*24,24); # Tage, Stunden" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#T2G$\"+=0;RT!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6$$\"+++++S!\"*$\"*V_)RL!\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 97 " \+ 9. Zeitpunkte, f\374r die in einem Abstand von 3 Tagen die Wachstum sgeschwindigkeit gleich ist.\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "t1:= fsolve( f(x)=f(x+3),x=0..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t1G$\"+/v];')!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "t2:=t1+3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t2G$\" +]2lhQ!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 139 " 10. Zeitpunkt, \+ wann die Pflanze nicht mehr wachsen w\374rde, wenn nach 10 Tagen die \+ \304nderung der Wachstumsgeschwindigkeit konstant bliebe." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " x0:=4; # Stelle " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x0G\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "tangente:=unapply(f1(x0)*(x-x0)+f(x 0),x);" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)tangenteGf*6#%\"xG6\"6$%)operatorG%&arrowGF(,&* (\"#S\"\"\"-%$expG6#!\"#F/,&9$F/\"\"%!\"\"F/F7*&\"$g\"F/F0F/F/F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "T3:=fsolve( tangente(x)=0 ,x=0..20);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#T3G$\"+********z!\"* " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "div(T3*24,24); # Tage, \+ Stunden" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"+++++!)!\"*$\"\"!F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " 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