{VERSION 3 0 "IBM INTEL NT" "3.0" }
{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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 
"" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 12 0 0 0 0 
1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 
}{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 
261 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 
0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 
0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 
265 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 
0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 
0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 
269 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 
0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 
0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
273 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 
0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 
0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
277 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 
0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 
0 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
281 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 282 "" 0 1 0 0 0 
0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 283 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 
0 }{CSTYLE "" -1 284 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
285 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 286 "" 0 1 0 0 0 
0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 287 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 
0 }{CSTYLE "" -1 288 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 
289 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 290 "" 0 1 0 0 0 
0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 291 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 
0 }{CSTYLE "" -1 292 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 
293 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 294 "" 0 1 0 0 0 
0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 295 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 
0 }{CSTYLE "" -1 296 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
297 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 298 "" 0 1 0 0 0 
0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 299 "" 0 1 0 0 0 0 1 0 0 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 8 4 0 0 0 
0 0 0 -1 0 }}
{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 9 "         " }}{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 33 "INSTRUCTIONS (Click box in front)" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1192 "
It is strongly suggested that this project be worked in teams (of up t
o 3  persons). Approaches may be discussed among different teams, but \+
each team must write their OWN report.\nREQUIREMENTS OF REPORT:\n- Mat
hematical contents (correctness and completeness) counts most. Solve t
he problems and show all essential calculations (commands and output) \+
and plots. Please do not submit work that is not essential (e.g. check
ing out how the function fplot in Problem 1 works - this may be essent
ial to your understanding, but it s not essential for the reader).\n- \+
Explain the steps you carry out. Explain the approaches/techniques tha
t you use.\n- Add explanations and answer questions where asked to do \+
so. By all means, include additional explanations/observations/conclus
ions that come to your mind! (This could translate to extra credit.)\n
HOW TO SUBMIT THE REPORT\nEach team submits ONE printed copy (stapled)
 by the due date. (Please save the electronic version, as you will be \+
asked to submit that, too, at a future time.)\nYou can print from insi
de your Maple worksheet (choose File/Print or click on the printer but
ton). Set the ZOOM FACTOR to 100% (smallest magnifying glass) before p
rinting.\n" }{TEXT 256 62 "Please remove these instructions before sub
mitting the report." }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "rest
art:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 147 "For this problem, you ma
y find it useful to name the solutions to the equations that you solve
 and use these names instead of typing the solutions." }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 268 7 "EXAMPLE" }{TEXT 269 0 
"" }{TEXT -1 72 "  Find the equation of the tangent line(s) to the gra
ph of the function " }{TEXT 274 1 "f" }{TEXT -1 1 "(" }{TEXT 270 1 "x
" }{TEXT -1 4 ") = " }{XPPEDIT 18 0 "4*x^3-15*x^2-18*x+10;" "6#,**&\"
\"%\"\"\"*$%\"xG\"\"$F&F&*&\"#:F&*$F(\"\"#F&!\"\"*&\"#=F&F(F&F.\"#5F&
" }{TEXT -1 24 " which has a slope of 6." }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "To find the " }{TEXT 271 1 "x" }
{TEXT -1 57 "-coordinate of the point(s) to the graph of the function \+
" }{TEXT 275 1 "f" }{TEXT -1 73 " where the slope of the tangent line \+
is 6, we want to solve the equation " }{TEXT 276 1 "f" }{TEXT -1 3 " '
(" }{TEXT 272 1 "x" }{TEXT -1 6 ") = 6." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 38 "f := x -> 4*x^3 - 15 *x^2 - 18*x + 10;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "D(f)(x);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 40 "We will use Maple to solv
e the equation " }{TEXT 277 1 "f" }{TEXT -1 3 " '(" }{TEXT 273 1 "x" }
{TEXT -1 35 ") = 6 and store the solution(s) to " }{TEXT 278 3 "sol" }
{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "D(f)(x) = \+
6;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "solve(D(f)(x)=6); sol
 := %;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 67 "By typing sol[1], we will get the first listed solution, \+
which is  " }{XPPEDIT 18 0 "5/4+1/4*sqrt(57);" "6#,&*&\"\"&\"\"\"\"\"%
!\"\"F&*(\"\"\"F&\"\"%F(-%%sqrtG6#\"#dF&F&" }{TEXT -1 74 "  and by typ
ing sol[2], we will get the second listed solution, which is  " }
{XPPEDIT 18 0 "5/4-1/4*sqrt(57);" "6#,&*&\"\"&\"\"\"\"\"%!\"\"F&*(\"\"
\"F&\"\"%F(-%%sqrtG6#\"#dF&F(" }{TEXT -1 115 " .  Of course, if there \+
would have been a third solution to the equation, we would type sol[3]
 to get it and so on." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "so
l[1]; sol[2];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 47 "One of the points on the graph of the function " }
{TEXT 279 1 "f" }{TEXT -1 55 ", where the tangent line has a slope of \+
6, is the point" }}{PARA 0 "" 0 "" {TEXT -1 2 "( " }{XPPEDIT 18 0 "5/4
+1/4*sqrt(57);" "6#,&*&\"\"&\"\"\"\"\"%!\"\"F&*(\"\"\"F&\"\"%F(-%%sqrt
G6#\"#dF&F&" }{TEXT -1 3 " , " }{TEXT 280 1 "f" }{TEXT -1 3 " ( " }
{XPPEDIT 18 0 "5/4+1/4*sqrt(57);" "6#,&*&\"\"&\"\"\"\"\"%!\"\"F&*(\"\"
\"F&\"\"%F(-%%sqrtG6#\"#dF&F&" }{TEXT -1 60 " ) ).  Using the name giv
en to the solutions, the solution  " }{XPPEDIT 18 0 "5/4+1/4*sqrt(57);
" "6#,&*&\"\"&\"\"\"\"\"%!\"\"F&*(\"\"\"F&\"\"%F(-%%sqrtG6#\"#dF&F&" }
{TEXT -1 154 "  has the name of sol[1].  So, we could simply type ( so
l[1], f (sol[1]) ) for this point.  Similarly, we could type ( sol[2],
 f (sol[2]) ) for the point " }}{PARA 0 "" 0 "" {TEXT -1 2 "( " }
{XPPEDIT 18 0 "5/4-1/4*sqrt(57);" "6#,&*&\"\"&\"\"\"\"\"%!\"\"F&*(\"\"
\"F&\"\"%F(-%%sqrtG6#\"#dF&F(" }{TEXT -1 3 " , " }{TEXT 281 1 "f" }
{TEXT -1 3 " ( " }{XPPEDIT 18 0 "5/4-1/4*sqrt(57);" "6#,&*&\"\"&\"\"\"
\"\"%!\"\"F&*(\"\"\"F&\"\"%F(-%%sqrtG6#\"#dF&F(" }{TEXT -1 103 " ) ) w
hich is the other point on the graph of  the function f where the slop
e of the tangent line is 6." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 62 "The equation of the tangent line to the graph o
f the function " }{TEXT 285 1 "f" }{TEXT -1 24 " at the point ( sol[1]
, " }{TEXT 286 1 "f" }{TEXT -1 35 " (sol[1]) ) can be found by typing:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "y = D(f)(sol[1])*(x-sol
[1]) + f(sol[1]); simplify(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 62 "The equation of the tangent line to t
he graph of the function " }{TEXT 284 1 "f" }{TEXT -1 24 " at the poin
t ( sol[2], " }{TEXT 287 1 "f" }{TEXT -1 35 " (sol[2]) ) can be found \+
by typing:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "y = D(f)(sol[
2])*(x-sol[2]) + f(sol[2]); simplify(%);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 76 "NOTE:  In the two equatio
ns above, you could have just typed 6 instead of D(" }{TEXT 282 1 "f" 
}{TEXT -1 16 ")(sol[1]) and D(" }{TEXT 283 1 "f" }{TEXT -1 105 ")(sol[
2]) since you already know that the value of the derivative of f at so
l[1] and sol[2] is 6.  Right?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 26 "D(f)(sol[1]); simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 " D(f)(sol[2]); simplify(%);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 288 7 "
PROBLEM" }{TEXT -1 72 "  Find the equation of the tangent line(s) to t
he graph of the function " }{TEXT 293 1 "y" }{TEXT -1 3 " = " }
{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 299 1 "y" }{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)  Define the function " }{TEXT 294 1 "y" }{TEXT 
-1 20 " using Maple syntax:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "(b)  Find a nice g
raph of the function " }{TEXT 295 1 "y" }{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 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "(c
)  Find the " }{TEXT 292 5 "exact" }{TEXT -1 14 " value of the " }
{TEXT 289 1 "x" }{TEXT -1 57 "-coordinate of the point(s) on the graph
 of the function " }{TEXT 296 1 "y" }{TEXT -1 42 " where the tangent l
ine has a slope of 21." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 5 "     " }{TEXT 290 19 "Answer to Part (c) " }{TEXT 291 7 
"       " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 75 "(d)  Find the equation of the tangent line(s) to the grap
h of the function " }{TEXT 297 1 "y" }{TEXT -1 25 " which has a slope \+
of 21." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "(e)  Graph the \+
function " }{TEXT 298 1 "y" }{TEXT -1 54 " and the tangent lines in Pa
rt (d) above on one graph." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}}{MARK "34 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }