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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Lesson 1 Maple Activities \+
for August 31:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }{TEXT 257 9 "Example 1" }{TEXT -1 23 "  Solve the inequ
ality " }{XPPEDIT 18 0 "x^2+3*x;" "6#,&*$%\"xG\"\"#\"\"\"*&\"\"$F'F%F'
F'" }{TEXT -1 72 " >= 0 graphically using Maple.  NOTE:  This is Probl
em 2 from Handout 1." }}{PARA 0 "" 0 "" {TEXT 256 0 "" }{TEXT -1 0 "" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 64 
"There are two parts to this problem: (a) solving the inequality " }
{XPPEDIT 18 0 "x^2+3*x;" "6#,&*$%\"xG\"\"#\"\"\"*&\"\"$F'F%F'F'" }
{TEXT -1 34 " > 0 and (b) solving the equation " }{XPPEDIT 18 0 "x^2+3
*x;" "6#,&*$%\"xG\"\"#\"\"\"*&\"\"$F'F%F'F'" }{TEXT -1 91 " = 0.  The \+
solution to both parts can be obtained graphically by graphing the equ
ation y = " }{XPPEDIT 18 0 "x^2+3*x;" "6#,&*$%\"xG\"\"#\"\"\"*&\"\"$F'
F%F'F'" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(x^2 + 3*x, x);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 98 "Of course
, the graph of the equation is a parabola.  Let's zoom in on where the
 graph crosses the " }{TEXT 263 1 "x" }{TEXT -1 71 "-axis.  We will st
ore this graph to \"p\" in order to use it later below." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot(x
^2 + 3*x, x=-6..4); p := %:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 69 "The y-coordinate of the points on the gr
aph represent the expression " }{XPPEDIT 18 0 "x^2+3*x;" "6#,&*$%\"xG
\"\"#\"\"\"*&\"\"$F'F%F'F'" }{TEXT -1 45 " since this is the graph of \+
the equation y = " }{XPPEDIT 18 0 "x^2+3*x;" "6#,&*$%\"xG\"\"#\"\"\"*&
\"\"$F'F%F'F'" }{TEXT -1 2 " ." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "
." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 31 "Answ
er the following questions:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 28 "1.  Where is the expression " }{XPPEDIT 18 0 "x
^2+3*x;" "6#,&*$%\"xG\"\"#\"\"\"*&\"\"$F'F%F'F'" }{TEXT -1 5 " = 0?" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 17 "2.  What
 are the " }{TEXT 264 1 "x" }{TEXT -1 34 "-intercept(s) of the equatio
n y = " }{XPPEDIT 18 0 "x^2+3*x;" "6#,&*$%\"xG\"\"#\"\"\"*&\"\"$F'F%F'
F'" }{TEXT -1 1 "?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 28 "3.  Where is the expression " }{XPPEDIT 18 0 "x^2+3*x;" "
6#,&*$%\"xG\"\"#\"\"\"*&\"\"$F'F%F'F'" }{TEXT -1 5 " > 0?" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "4.  Where is the e
xpression " }{XPPEDIT 18 0 "x^2+3*x;" "6#,&*$%\"xG\"\"#\"\"\"*&\"\"$F'
F%F'F'" }{TEXT -1 5 " < 0?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 43 "5.  What is the solution to the inequality " }
{XPPEDIT 18 0 "x^2+3*x;" "6#,&*$%\"xG\"\"#\"\"\"*&\"\"$F'F%F'F'" }
{TEXT -1 6 " >= 0?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 55 "Now, we will plot the x-intercepts of the equatio
n y = " }{XPPEDIT 18 0 "x^2+3*x;" "6#,&*$%\"xG\"\"#\"\"\"*&\"\"$F'F%F'
F'" }{TEXT -1 52 " which we answered above.  First, we will plot each \+
" }{TEXT 265 1 "x" }{TEXT -1 35 "-intercept individually.  Plot the " 
}{TEXT 266 1 "x" }{TEXT -1 19 "-intercept (-3, 0)." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "plot([[-3,0
]], style=point, symbol=box, color=blue);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 19 "Now plot the other " }
{TEXT 267 1 "x" }{TEXT -1 84 "-intercept of (0,0).  Copy the plot comm
and above for (-3,0) and change the -3 to 0." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "plot([[0,0]], sty
le=point, symbol=box, color=blue);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "Now, let's plot the two " }
{TEXT 269 1 "x" }{TEXT -1 53 "-intercepts with one command and store t
his to \"pts\"." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 71 "plot([ [-3,0], [0,0] ], style=point, symbol=bo
x, color=blue); pts := %:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 61 "Now, we will plot the parabola that was s
aved to \"p\" and the " }{TEXT 268 1 "x" }{TEXT -1 65 "-intercepts tha
t were saved to \"pts\" using the withplots command." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plot
s):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "display(p,pts);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 71 "No
w, let's ask Maple to solve the inequality with the following command
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "solve(x^2+3*x >= 0);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 131 "We need to be careful in
 reading this answer.  The two endpoints of  - 3  and 0 are included i
n this Maple answer because the word " }{TEXT 270 4 "Open" }{TEXT -1 
119 " is not in front of the two numbers.  If an endpoint is not to be
 included in the answer, then Maple will put the word " }{TEXT 288 4 "
Open" }{TEXT -1 24 " in front of the number " }{TEXT 289 3 "and" }
{TEXT -1 24 " will put the number in " }{TEXT 290 11 "parentheses" }
{TEXT -1 1 "." }{TEXT -1 64 "   Look at the Maple answer for the solut
ion of the inequality  " }{XPPEDIT 18 0 "x^2+3*x;" "6#,&*$%\"xG\"\"#\"
\"\"*&\"\"$F'F%F'F'" }{TEXT -1 5 " > 0." }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(x^2+3*x > 0);" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 9 "T
he word " }{TEXT 271 4 "Open" }{TEXT -1 68 " in front of the numbers o
f  - 3 and 0 means that the two endpoints " }{TEXT 272 7 "are not" }
{TEXT -1 24 " included in the answer." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 259 
9 "Example 2" }{TEXT -1 23 "  Solve the inequality " }{XPPEDIT 18 0 "x
^4-2*x^3-7*x^2+8*x+12;" "6#,,*$%\"xG\"\"%\"\"\"*&\"\"#F'*$F%\"\"$F'!\"
\"*&\"\"(F'*$F%\"\"#F'F,*&\"\")F'F%F'F'\"#7F'" }{TEXT -1 48 " < 0.  NO
TE:  This is Problem 16 from Handout 1." }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }{TEXT 258 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 41 "Zoom in on the graph in order to see the " }{TEXT 
273 1 "x" }{TEXT -1 14 "-intercept(s)." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "plot(x^4 - 2*x^3 - 7*x^
2 + 8*x + 12,x=-4..4);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 31 "Answer the following questions:" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 17 "1.  What are th
e " }{TEXT 274 1 "x" }{TEXT -1 12 "-intercepts?" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "2.  What is the solution \+
to the inequality " }{XPPEDIT 18 0 "x^4-2*x^3-7*x^2+8*x+12;" "6#,,*$%
\"xG\"\"%\"\"\"*&\"\"#F'*$F%\"\"$F'!\"\"*&\"\"(F'*$F%\"\"#F'F,*&\"\")F
'F%F'F'\"#7F'" }{TEXT -1 5 " < 0?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 56 "3.  Why are the endpoints of the interval
s not included?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 32 "Now, we will solve the equation " }{XPPEDIT 18 0 "x^4-2*x
^3-7*x^2+8*x+12;" "6#,,*$%\"xG\"\"%\"\"\"*&\"\"#F'*$F%\"\"$F'!\"\"*&\"
\"(F'*$F%\"\"#F'F,*&\"\")F'F%F'F'\"#7F'" }{TEXT -1 15 " = 0 using the \+
" }{TEXT 260 5 "solve" }{TEXT -1 18 " command in Maple." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "solve(
x^4-2*x^3-7*x^2+8*x+12=0);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 36 "Thus, the solutions to the equation " }
{XPPEDIT 18 0 "x^4-2*x^3-7*x^2+8*x+12;" "6#,,*$%\"xG\"\"%\"\"\"*&\"\"#
F'*$F%\"\"$F'!\"\"*&\"\"(F'*$F%\"\"#F'F,*&\"\")F'F%F'F'\"#7F'" }{TEXT 
-1 50 " = 0 are -2, -1, 2, 3.  Now, solve the inequality " }{XPPEDIT 
18 0 "x^4-2*x^3-7*x^2+8*x+12;" "6#,,*$%\"xG\"\"%\"\"\"*&\"\"#F'*$F%\"
\"$F'!\"\"*&\"\"(F'*$F%\"\"#F'F,*&\"\")F'F%F'F'\"#7F'" }{TEXT -1 15 " \+
< 0 using the " }{TEXT 275 5 "solve" }{TEXT -1 9 " command." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 44 "Now, do the following problems for practice:" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
{TEXT 261 9 "Problem 1" }{TEXT -1 23 "  Solve the inequality " }
{XPPEDIT 18 0 "x^3+x^2-2*x;" "6#,(*$%\"xG\"\"$\"\"\"*$F%\"\"#F'*&\"\"#
F'F%F'!\"\"" }{TEXT -1 28 " > 0 graphically.  Show the " }{TEXT 276 1 
"x" }{TEXT -1 66 "-intercept(s) like we did in Example 1 above.  You c
an verify the " }{TEXT 278 1 "x" }{TEXT -1 19 "-coordinate of the " }
{TEXT 277 1 "x" }{TEXT -1 24 "-intercept(s) using the " }{TEXT 262 5 "
solve" }{TEXT -1 42 " command.  Verify your solution using the " }
{TEXT 279 5 "solve" }{TEXT -1 33 " command to solve the inequality." }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT 280 9 "Problem 2" }{TEXT -1 23 "  Solve the in
equality " }{XPPEDIT 18 0 "(3*x-2)/(18+3*x-x^2) <= 0;" "6#1*&,&*&\"\"$
\"\"\"%\"xGF(F(\"\"#!\"\"F(,(\"#=F(*&\"\"$F(F)F(F(*$F)\"\"#F+F+\"\"!" 
}{TEXT -1 24 " graphically.  Show the " }{TEXT 282 1 "x" }{TEXT -1 66 
"-intercept(s) like we did in Example 1 above.  You can verify the " }
{TEXT 284 1 "x" }{TEXT -1 19 "-coordinate of the " }{TEXT 283 1 "x" }
{TEXT -1 24 "-intercept(s) using the " }{TEXT 281 5 "solve" }{TEXT -1 
42 " command.  Verify your solution using the " }{TEXT 285 5 "solve" }
{TEXT -1 33 " command to solve the inequality." }{TEXT 286 2 "  " }
{TEXT -1 0 "" }{TEXT 287 57 "Turn in Problem 2 on Thursday, September \+
7, to be graded." }}{PARA 0 "" 0 "" {TEXT -1 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 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "2 0 0" 19 }
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