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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 259 10 "MATH-1850 " }{TEXT -1 3 "
   " }{TEXT 260 18 "COMPUTER PROBLEM 6" }{TEXT -1 55 "     DUE:  Tuesd
ay, October 24, 2000, in your lab class" }}{PARA 0 "" 0 "" {TEXT -1 
17 "\nTeam members:   " }{TEXT 267 54 "(All lines for answers below wi
ll extend as you type.)" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 16 "          (1)   " }{TEXT 261 0 "" }
{TEXT -1 0 "" }{TEXT 264 17 "    SOLUTION     " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "          (2)   " }{TEXT 
262 0 "" }{TEXT -1 0 "" }{TEXT 265 9 "         " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "          (3)   " }{TEXT 
263 0 "" }{TEXT -1 0 "" }{TEXT 266 9 "         " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "Score:               / 6
\n" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 258 13 "INSTRUCTIONS " }{TEXT 
257 20 "(Click box in front)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 1192 "It is strongly suggested that th
is project be worked in teams (of up to 3  persons). Approaches may be
 discussed among different teams, but each team must write their OWN r
eport.\nREQUIREMENTS OF REPORT:\n- Mathematical contents (correctness \+
and completeness) counts most. Solve the problems and show all essenti
al calculations (commands and output) and plots. Please do not submit \+
work that is not essential (e.g. checking out how the function fplot i
n Problem 1 works - this may be essential to your understanding, but i
t s not essential for the reader).\n- Explain the steps you carry out.
 Explain the approaches/techniques that you use.\n- Add explanations a
nd answer questions where asked to do so. By all means, include additi
onal explanations/observations/conclusions that come to your mind! (Th
is could translate to extra credit.)\nHOW TO SUBMIT THE REPORT\nEach t
eam submits ONE printed copy (stapled) by the due date. (Please save t
he electronic version, as you will be asked to submit that, too, at a \+
future time.)\nYou can print from inside your Maple worksheet (choose \+
File/Print or click on the printer button). Set the ZOOM FACTOR to 100
% (smallest magnifying glass) before printing.\n" }{TEXT 256 62 "Pleas
e remove these instructions before submitting the report." }}}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 289 7 "PROBLEM" }{TEXT -1 73 "  Find the equation of the tangent
 line(s) to the graph of the function  " }{TEXT 290 1 "f" }{TEXT -1 1 
"(" }{TEXT 274 1 "x" }{TEXT -1 4 ") = " }{XPPEDIT 18 0 "x^5-5*x^3+8;" 
"6#,(*$%\"xG\"\"&\"\"\"*&\"\"&F'*$F%\"\"$F'!\"\"\"\")F'" }{TEXT -1 53 
"  which has a slope of 21 .  Then graph the function " }{TEXT 291 1 "
f" }{TEXT -1 38 " and the tangent line(s) on one graph." }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "(a)  Defi
ne the function " }{TEXT 256 1 "f" }{TEXT -1 20 " using Maple syntax:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "f := x -> x^5 - 5*x^3 +
 8;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%
&arrowGF(,(*$)9$\"\"&\"\"\"\"\"\"*$)F/\"\"$F1!\"&\"\")F2F(F(F(" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "(b
)  Find a nice graph of the function " }{TEXT 256 1 "f" }{TEXT -1 20 "
 by restricting the " }{TEXT 257 1 "x" }{TEXT -1 8 " and/or " }{TEXT 
258 1 "y" }{TEXT -1 8 " values." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 30 "plot(f(x),x=-4..4, y=-40..40);" }}{PARA 13 "" 1 "" {GLPLOT2D 
400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7W7$$!\"%\"\"!$!$'pF*7$$!1MLL$Q
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hN2-IF0$!11:J)H3c+\"F37$$!1+++N&oz$GF0$!1)\\*f`Nt!='!#97$$!1nmm\")3DoE
F0$!1()>'4o'[EKFfn7$$!1+++:v2*\\#F0$!1,kd7hwV6Ffn7$$!1LLL8>1DBF0$\"1A1
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_;F37$$\"1nmmc%GpL$F0$\"1Bzj*=;'fBF37$$\"1LLL8-V&\\$F0$\"1C?Yi_iiJF37$
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45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 14 "(c)  Find the " }{TEXT 297 5 "exact" }
{TEXT -1 14 " value of the " }{TEXT 293 1 "x" }{TEXT -1 57 "-coordinat
e of the point(s) on the graph of the function " }{TEXT 294 1 "f" }
{TEXT -1 42 " where the tangent line has a slope of 21." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "solve(D(f)(x)=21); sol := %; evalf(
%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&,$*$-%%sqrtG6#,&\"$]\"\"\"\"*$-
F&6#\"$X'\"\"\"\"#5F/#F*F0,$F$#!\"\"F0,$*$-F&6#,&F)F*F+!#5F/F1,$F6F3" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG6&,$*$-%%sqrtG6#,&\"$]\"\"\"
\"*$-F)6#\"$X'\"\"\"\"#5F2#F-F3,$F'#!\"\"F3,$*$-F)6#,&F,F-F.!#5F2F4,$F
9F6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&$\"+on*)4?!\"*$!+on*)4?F%,$%\"I
G$\"+f%\\'>5F%,$F)$!+f%\\'>5F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "
     " }}{PARA 0 "" 0 "" {TEXT 295 23 "    Answer to Part (c) " }
{TEXT 296 3 "   " }{XPPEDIT 18 0 "1/10*sqrt(150+10*sqrt(645))-1/10*sqr
t(150+10*sqrt(645));" "6$,$*$-%%sqrtG6#,&\"$]\"\"\"\"*$-F&6#\"$X'\"\"
\"\"#5F/#F*F0,$F$#!\"\"F0" }{TEXT 298 3 "   " }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 75 "(d)  Find the equation \+
of the tangent line(s) to the graph of the function " }{TEXT 292 1 "f
" }{TEXT -1 25 " which has a slope of 21." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 51 "y = D(f)(sol[1])*(x-sol[1])+f(sol[1]); simplify(%);
" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/%\"yG,**&,(*$),&\"$]\"\"\"\"*$-%%
sqrtG6#\"$X'\"\"\"\"#5\"\"#F2#F,\"%+?#!#XF4F,F-#!\"$F4F,,&%\"xGF,*$-F/
6#F*F2#!\"\"F3F,F,*$)F*#\"\"&F4F2#F,\"'++5*$)F*#\"\"$F4F2#FA\"$+#\"\")
F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"yG,*%\"xG\"#@*$-%%sqrtG6#,&
\"$]\"\"\"\"*$-F*6#\"$X'\"\"\"\"#5F3#!#**\"#]*&F)F3F0F3#!\"\"F7\"\")F.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 51 "y = D(f)(sol[2])*(x-sol[2])+f(sol[2]); simplif
y(%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/%\"yG,**&,(*$),&\"$]\"\"\"\"
*$-%%sqrtG6#\"$X'\"\"\"\"#5\"\"#F2#F,\"%+?#!#XF4F,F-#!\"$F4F,,&%\"xGF,
*$-F/6#F*F2#F,F3F,F,*$)F*#\"\"&F4F2#!\"\"\"'++5*$)F*#\"\"$F4F2#F,\"$+#
\"\")F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"yG,*%\"xG\"#@*$-%%sqrtG
6#,&\"$]\"\"\"\"*$-F*6#\"$X'\"\"\"\"#5F3#\"#**\"#]*&F)F3F0F3#F.F7\"\")
F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
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he tangent lines in Part (d) above on one graph." }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 127 "plot([f(x), D(f)(sol[1])*(x-sol[1])+f(sol[1]
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