{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 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 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }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 1 }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 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "T itle" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 13 "Maple Syntax " }}{PARA 0 "" 0 "" {TEXT -1 10 "Problem 5." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "A:=proc(x) 2*x*sqrt(25-x^2) end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGR6#%\"xG6\"F(F(,$*&9$\"\"\"-%%sqrtG6#,&\"#DF,*$)F+\"\"#F,! \"\"F,F4F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "A(x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%\"xG\"\"\"-%%sqrtG6#,&\"#DF&*$)F% \"\"#F&!\"\"F&F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "A1:=pro c(x) diff(A(x),x) end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1GR6#%\" xG6\"F(F(-%%diffG6$-%\"AG6#9$F/F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "A1(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$-%%sqrtG 6#,&\"#D\"\"\"*$)%\"xG\"\"#F*!\"\"F*F.*&*$F,F*F**$-F&6#F(F*F/!\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot(A1(x),x=-6..6);" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7W7$ $!1+++b'fs*\\!#:$!1*>gbc8U,$!#87$$!1+++5mC*)\\F*$!1T)y%*)eX7:F-7$$!1++ +kNB\")\\F*$!1lfAvu'z8\"F-7$$!1+++=0At\\F*$!1MlSqpGo%*!#97$$!1+++ru?l \\F*$!1,.=x'efD)F=7$$!1+++z8=\\\\F*$!15UH]0NZnF=7$$!1+++&GbJ$\\F*$!1oR 'zRm,\"eF=7$$!1++++J5,\\F*$!1VMSY'Rql%F=7$$!1+++940p[F*$!1&H)\\ym`VRF= 7$$!1+++Vl%\\![F*$!1c#GwDZB1$F=7$$!1+++s@%3u%F*$!17Pcii%F*$!18hZ@)*ze=F=7$$!1+++U.6.XF*$!16UI'\\VF*7$$!1+++5'f))*HF*$\"1%fV'y:41NF*7$$!1+++]J(*Q FF*$\"1\\*[2c'HzZF*7$$!1+++!RC&)[#F*$\"1rA)ya5v\"eF*7$$!1+++AH4hAF*$\" 1\"GjAP8ii'F*7$$!1+++5\\l!*>F*$\"1\"\\K*yANXuF*7$$!1+++S%e:w\"F*$\"1/P &=.bD.)F*7$$!1+++#yk]\\\"F*$\"1DS\"p\\Obg)F*7$$!1+++SF$>8&)*F*7$$!1+++?BI1EF^q$\"1LX0**o>f**F*7$ $!1++++]2Bf!#=$\"1>sH]*y*****F*7$$\"1+++!ygke#F^q$\"1dOk'[;)f**F*7$$\" 1+++IIa*)[F^q$\"14#zIyyf&)*F*7$$\"1+++]\\$pP(F^q$\"1%4M&4wZq'*F*7$$\"1 ++++UlY**F^q$\"1\\c)4-;jR*F*7$$\"1+++:B1Y7F*$\"1>V**3g=V!*F*7$$\"1+++Q F*7$$\"1+++gzs+SF*$!1heV2b%fn%F*7$$\"1+++ 5\"Q_D%F*$!1[6wZ!QEa)F*7$$\"1+++X%R9Q%F*$!1K+JUm-76F=7$$\"1+++!ySw]%F* $!15bPR*>bW\"F=7$$\"1+++?EdRZF*$!13NeSKU-DF=7$%%FAILGF[\\l-%'COLOURG6& %$RGBG$\"#5!\"\"\"\"!Fc\\l-%+AXESLABELSG6$Q\"x6\"%!G-%%VIEWG6$;$!\"'Fc \\l$\"\"'Fc\\l%(DEFAULTG" 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 21 " fsolve(A1(x),x,2..4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+1R`NN!\"* " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "subs(x=3,A1(x)); ## thi s is to find A1(3)##" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$-%%sqrtG6# \"#;\"\"\"#\"\"(\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "ev alf(%); ## this is to find the numerical value of the previous express ion.##" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+++++N!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Problem 1." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "r:=proc(t) sqrt(1.01*t^4-6.72*t^3+4.85*t^2+2.4*t+330. 26) end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rGR6#%\"tG6\"F(F(-%%sq rtG6#,,*$)9$\"\"%\"\"\"$\"$,\"!\"#*&$\"$s'F4F1)F/\"\"$F1!\"\"*&$\"$&[F 4F1)F/\"\"#F1F1*&$\"#CF:F1F/F1F1$\"&EI$F4F1F(F(F(" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 5 "r(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$-% %sqrtG6#,,*$)%\"tG\"\"%\"\"\"$\"$,\"!\"#*&$\"$s'F/F,)F*\"\"$F,!\"\"*&$ \"$&[F/F,)F*\"\"#F,F,*&$\"#CF5F,F*F,F,$\"&EI$F/F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "r1:=proc(t) diff(r(t),t) end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r1GR6#%\"tG6\"F(F(-%%diffG6$-%\"rG6#9$F/F (F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "r1(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,**$)%\"tG\"\"$\"\"\"$\"$/%!\"#*&$\"%;?F-F* )F(\"\"#F*!\"\"*&$\"$q*F-F*F(F*F*$\"#CF3F*F**$-%%sqrtG6#,,*$)F(\"\"%F* $\"$,\"F-*&$\"$s'F-F*F'F*F3*&$\"$&[F-F*F1F*F**&F7F*F(F*F*$\"&EI$F-F*F* F3#F*F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "r2:=proc(t) diff (r1(t),t) end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r2GR6#%\"tG6\"F(F (-%%diffG6$-%#r1G6#9$F/F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "r2(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&*$),**$)%\"tG\"\"$ \"\"\"$\"$/%!\"#*&$\"%;?F/F,)F*\"\"#F,!\"\"*&$\"$q*F/F,F*F,F,$\"#CF5F, F4F,F,*$),,*$)F*\"\"%F,$\"$,\"F/*&$\"$s'F/F,F)F,F5*&$\"$&[F/F,F3F,F,*& F9F,F*F,F,$\"&EI$F/F,#F+F4F,F5#F5F@*&*&#F,F4F,,(*$F3F,$\"%77F/*&$\"%KS F/F,F*F,F5F7F,F,F,*$-%%sqrtG6#F=F,F5F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plot(r(t),t=0..5);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7W7$$\"\"!F)$\"3!Qg/!)p0t\"=!#;7$$ \"3GLLL3x&)*3\"!#=$\"3BjSh0,;==F,7$$\"3umm\"H2P\"Q?F0$\"3$zr`SC`!>=F,7 $$\"3MLL$eRwX5$F0$\"3Oy6q[A6?=F,7$$\"33ML$3x%3yTF0$\"3;-*R$>h7@=F,7$$ \"3emm\"z%4\\Y_F0$\"3X!RXBbx>#=F,7$$\"3`LLeR-/PiF0$\"3siu'>5UD#=F,7$$ \"3]***\\il'pisF0$\"3W_K2U=#G#=F,7$$\"3>MLe*)>VB$)F0$\"3%yr$pB1rA=F,7$ $\"3Y++DJbw!Q*F0$\"3!y%pKYa7A=F,7$$\"3%ommTIOo/\"!#<$\"3'Hg_)fW'4#=F,7 $$\"3YLL3_>jU6Fhn$\"3>!\\5S&fU>=F,7$$\"37++]i^Z]7Fhn$\"3\"o(\\'>zqq\"= F,7$$\"33++](=h(e8Fhn$\"3A3C,W;+9=F,7$$\"3/++]P[6j9Fhn$\"3H)[\"f\"HW. \"=F,7$$\"3UL$e*[z(yb\"Fhn$\"3%)Ho2%*zS1=F,7$$\"3wmm;a/cq;Fhn$\"3)*fgC fv%4!=F,7$$\"3%ommmJFhn$\"3G%*fzWE(=y\"F,7$$\"3K+]i!f#=$3#Fhn$ \"3Ee$f$=Ajtpxg#Fhn$\"3dV%py)eZB>IFhn$\"3gX'=nu'Rv;F,7$$\"3F+]i!RU07$ Fhn$\"3G\\S#yluHm\"F,7$$\"3+++v=S2LKFhn$\"3_[%)yhu9\\;F,7$$\"3Jmmm\"p) =MLFhn$\"33,ugJ%=oj\"F,7$$\"3B++](=]@W$Fhn$\"3!*H;@yF!Ri\"F,7$$\"35L$e *[$z*RNFhn$\"3`Y)=*>Rc\"F,7 $$\"3yLLL$)*pp;%Fhn$\"3M=0+T95e:F,7$$\"3)RL$3xe,tUFhn$\"3k)QWyz(*Rb\"F ,7$$\"3h+v=n(*fDVFhn$\"35?b\" F,7$$\"3MMe9\"z-lU%Fhn$\"3=S&yUwx=b\"F,7$$\"3a+++D>#[Z%Fhn$\"3WSsAkFD_ :F,7$$\"3TM$3_5,-`%Fhn$\"3!fx.2F\\Lb\"F,7$$\"3SnmT&G!e&e%Fhn$\"3S>\")y :C>b:F,7$$\"3m+]P%37^j%Fhn$\"3)*\\X1.E]d:F,7$$\"3#RLLL)Qk%o%Fhn$\"3yX< c-OYg:F,7$$\"37+]iSjE!z%Fhn$\"35d\"*\\#Gj!p:F,7$$\"3a+]P40O\"*[Fhn$\"3 ?DGo5+Q!e\"F,7$$\"\"&F)$\"3'>I=iH?hf\"F,-%'COLOURG6&%$RGBG$\"#5!\"\"F( F(-%+AXESLABELSG6$Q\"t6\"Q!6\"-%%VIEWG6$;F(Fi[l%(DEFAULTG" 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 11 "Questions: " }}{PARA 0 "" 0 "" {TEXT -1 59 "(1) How do we find the max and min for r(t) by using r'(t)?" }} {PARA 0 "" 0 "" {TEXT -1 67 "(2) How do we find the year which interes t rate decreases the most?" }}{PARA 0 "" 0 "" {TEXT -1 67 "(3) How do \+ we find the year which interest rate increases the most?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(r1(t),t=0..5);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7W7$$\"\"!F)$\"3 ?u'o%\\==.m!#>7$$\"3GLLL3x&)*3\"!#=$\"3#GF?)RFMLe*)>V B$)F0$!3%)\\@?fSN\">$F,7$$\"3Y++DJbw!Q*F0$!3m))HJClwuzF,7$$\"3%ommTIOo /\"!#<$!3alw#=+bkM\"F07$$\"3YLL3_>jU6Fin$!39(Ql!))ehr=F07$$\"37++]i^Z] 7Fin$!3\"*Q!*Rqjd-DF07$$\"33++](=h(e8Fin$!3YGk\">%RErJF07$$\"3/++]P[6j 9Fin$!3bKG(GG6?%QF07$$\"3UL$e*[z(yb\"Fin$!3KIUm)4hyY%F07$$\"3wmm;a/cq; Fin$!3h(3+V0-dA&F07$$\"3%ommmJFin$!3+gR)>tVbG(F07$$\"3K+]i!f#= $3#Fin$!35$)>^.pxg#Fin$!3/[DFWrN&4\"Fin7$$\"33+] Pf4t.FFin$!3'oa>xJ3b8\"Fin7$$\"3uLLe*Gst!GFin$!3'z;<#R)H?<\"Fin7$$\"30 +++DRW9HFin$!3By8C%Q#G,7Fin7$$\"3:++DJE>>IFin$!3xf\\QuB[?7Fin7$$\"3F+] i!RU07$Fin$!39/Doe@8H7Fin7$$\"3+++v=S2LKFin$!3F%4ppK%*fA\"Fin7$$\"3Jmm m\"p)=MLFin$!3cg03-V`57Fin7$$\"3B++](=]@W$Fin$!3[sGM(f#\\z6Fin7$$\"35L $e*[$z*RNFin$!3$3?+ScXs8\"Fin7$$\"3e++]iC$pk$Fin$!3)o4]$GrSu5Fin7$$\"3 [m;H2qcZPFin$!3oAhIc_0#)**F07$$\"3O+]7.\"fF&QFin$!3?21o\"Rgi**)F07$$\" 3Ymm;/OgbRFin$!3R$3j3!\\8MyF07$$\"3w**\\ilAFjSFin$!3?(eH,R;jR'F07$$\"3 yLLL$)*pp;%Fin$!3k1'[c$*o&)y%F07$$\"3)RL$3xe,tUFin$!34IF'y$Q+6HF07$$\" 3Cn;HdO=yVFin$!3n$)z7EQ^9\")F,7$$\"3a+++D>#[Z%Fin$\"3J`j+Q3aF8F07$$\"3 SnmT&G!e&e%Fin$\"3@Pqr^k&Q-%F07$$\"3m+]P%37^j%Fin$\"33r^Un'oEJ&F07$$\" 3#RLLL)Qk%o%Fin$\"3%o3\\FHR:l'F07$$\"3-n\"z>6but%Fin$\"3!*)4FN32H8)F07 $$\"37+]iSjE!z%Fin$\"3M,%RR\"HDo'*F07$$\"3L+++DM\"3%[Fin$\"38?=4v(f'=6 Fin7$$\"3a+]P40O\"*[Fin$\"3EDgBD:3v7Fin7$$\"3s+voa-oX\\Fin$\"3MDN\\@u0 [9Fin7$$\"\"&F)$\"3p[*ofI " 0 "" {MPLTEXT 1 0 19 "plot(r2(t),t=0..5);" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7S7$ $\"\"!F)$\"3wh()yInQmE!#=7$$\"3GLLL3x&)*3\"F,$\"3;%HjD3_V\\\"F,7$$\"3u mm\"H2P\"Q?F,$\"3O)Q\\7M.]S&!#>7$$\"3MLL$eRwX5$F,$!3/Mx6R#oYe%F77$$\"3 3ML$3x%3yTF,$!3cYc\\/fT&Q\"F,7$$\"3emm\"z%4\\Y_F,$!30CUEH)f.B#F,7$$\"3 `LLeR-/PiF,$!3]^2EB0bXHF,7$$\"3]***\\il'pisF,$!3)[%o1U\"[\"=OF,7$$\"3> MLe*)>VB$)F,$!32UxJCzUUUF,7$$\"3Y++DJbw!Q*F,$!3]:Sz]<*G&F,7$$\"3YLL3_>jU6Fhn$!3#*GHM*f,em&F,7$$\"37++]i ^Z]7Fhn$!3nAcqrI7CgF,7$$\"33++](=h(e8Fhn$!3A(36^B%y9jF,7$$\"3/++]P[6j9 Fhn$!3\"H2NV?\"))HlF,7$$\"3UL$e*[z(yb\"Fhn$!3_t\"R&=n4qmF,7$$\"3wmm;a/ cq;Fhn$!3AB')Qu1QonF,7$$\"3%ommmJFhn$!3EwVg()*GYl'F,7$$\"3K+]i!f#= $3#Fhn$!3#*))[s#)4(pZ'F,7$$\"3?+](=xpe=#Fhn$!3dA62yEsPiF,7$$\"37nm\"H2 8IH#Fhn$!3N')y9g>P7fF,7$$\"3um;zpSS\"R#Fhn$!3=Wt!o.#eUbF,7$$\"3GLL3_?` (\\#Fhn$!3wu6l)o!*Q1&F,7$$\"3fL$e*)>pxg#Fhn$!3#R\\._asWZ%F,7$$\"33+]Pf 4t.FFhn$!3w'3OL(['3)QF,7$$\"3uLLe*Gst!GFhn$!3]8*34Ty5:$F,7$$\"30+++DRW 9HFhn$!31M=l$fM`H#F,7$$\"3:++DJE>>IFhn$!39D'**euoFN\"F,7$$\"3F+]i!RU07 $Fhn$!39]$ong0qO$F77$$\"3+++v=S2LKFhn$\"3C%eC)eS*z;*F77$$\"3Jmmm\"p)=M LFhn$\"3K@Ao-X$)f@F,7$$\"3B++](=]@W$Fhn$\"3#z*4Ju]\\7OF,7$$\"35L$e*[$z *RNFhn$\"3!yzaB)4[U]F,7$$\"3e++]iC$pk$Fhn$\"3`f/)e]6'HnF,7$$\"3[m;H2qc ZPFhn$\"3\\C>_U\\/L%)F,7$$\"3O+]7.\"fF&QFhn$\"3\\c.+T8(G.\"Fhn7$$\"3Ym m;/OgbRFhn$\"3-'e9!>.uG7Fhn7$$\"3w**\\ilAFjSFhn$\"3$*yHqqihV9Fhn7$$\"3 yLLL$)*pp;%Fhn$\"3_\\k#[Z%Fhn$\"3pOCc3N*pJ#Fhn 7$$\"3SnmT&G!e&e%Fhn$\"3%)\\'f*=dHFhn7$$\"3a+]P40O\"*[Fhn$\"3Z!f '[%zJ'QJFhn7$$\"\"&F)$\"3H.gKKuq9LFhn-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(- %+AXESLABELSG6$Q\"t6\"Q!6\"-%%VIEWG6$;F(Fez%(DEFAULTG" 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 10 "Questions:" }}{PARA 0 "" 0 "" {TEXT -1 71 "(1) Ho w are the x-intercepts of r''(t) related to the max/min of r'(t)?" }} {PARA 0 "" 0 "" {TEXT -1 68 "(2) How are the x-intercepts of r''(t) re lated to the function r(t)?" }}{PARA 0 "" 0 "" {TEXT -1 48 "(3) Why in flection points are important to r(t)?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "23 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }