{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 "2D Output" 2 20 "" 0 1 0 0 255 1 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 "" 0 18 
0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 18 0 0 0 0 0 0 0 0 
0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 260 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 
261 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 1 14 0 0 
0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 1 14 0 0 0 0 0 1 0 0 0 0 
0 0 0 }{CSTYLE "" -1 264 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "
" -1 265 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 1 12 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 2 0 0 0 0 
0 0 0 0 }{CSTYLE "" -1 268 "" 0 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE 
"" -1 269 "" 0 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 
0 0 0 0 2 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 2 0 0 0 0 
0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 }{CSTYLE "
" -1 273 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 
0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 0 1 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 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 
0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading
 3" 4 5 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 }0 0 0 
-1 0 0 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 }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 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "
" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 
-1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 
0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }{TEXT 258 0 "" }{TEXT 
259 46 "Calc1_Sketching a Curve Using Its Derivatives " }{TEXT 256 0 "
" }{TEXT 257 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 262 0 "" }{TEXT 
263 18 "Calculus I Project" }{TEXT -1 0 "" }{TEXT 261 0 "" }{TEXT 260 
1 " " }}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" }{TEXT 264 0 "" }{TEXT 265 
10 "Objectives" }}{PARA 0 "" 0 "" {TEXT -1 243 "a) To use graphs of th
e first and second derivative of a function to determine critical poin
ts of the graph of the function, intervals in which the function incre
ases or     decreases, and intervals in which the function is concave \+
up or down." }}{PARA 0 "" 0 "" {TEXT -1 90 "b) To use the information \+
obtained to sketch a graph of the curve, given an initial value." }}
{PARA 0 "" 0 "" {TEXT -1 71 "Note: It is assumed that students have no
t yet studied antiderivatives." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 71 "Using Maple allows the student to visuali
ze and compare sets of graphs." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{PARA 3 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" 
}{TEXT 266 15 "Solved Example:" }}{PARA 0 "" 0 "" {TEXT -1 15 "Given f
 '(x) = " }{XPPEDIT 18 0 "3*x^2-4*x;" "6#,&*&\"\"$\"\"\"*$%\"xG\"\"#F&
F&*&\"\"%F&F(F&!\"\"" }{TEXT -1 20 "   and  f (0) = 1,  " }}{PARA 0 "
" 0 "" {TEXT -1 15 "a) find  f \"(x)" }}{PARA 0 "" 0 "" {TEXT -1 54 "b
) plot  f '(x)  and  f \"(x)  on the same set of axes." }}{PARA 0 "" 
0 "" {TEXT -1 78 "c) determine where:  f '(x) = 0,  f \"(x) = 0, and w
here f '(x) is not defined." }}{PARA 0 "" 0 "" {TEXT -1 89 "d) determi
ne the intervals for which:   f '(x) >0,  f '(x) < 0,  f \"(x) < 0,  f
 \"(x) > 0 " }}{PARA 0 "" 0 "" {TEXT -1 80 "e) organize the data in a \+
table and draw conclusions about the graph of   f (x)." }}{PARA 0 "" 
0 "" {TEXT -1 48 "f)  hand sketch  f (x)  using the initial value." }}
}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 3 "" 0 "" {TEXT -1 0 "" }}
{SECT 0 {PARA 5 "" 0 "" {TEXT -1 9 "Solution:" }{TEXT 267 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "firstder:=3*x^2 - 4*x;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)firstderG,&*$)%\"xG\"\"#\"\"\"\"\"$
F(!\"%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "secondder:=diff(3*x^2 - 4*x,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%*secondderG,&%\"xG\"\"'!\"%\"\"\"" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 113 "plot([firstder, secondder], x = -5..5, y =
 -5..5, color = [red,blue], title = \"graphs of 1st & 2nd derivatives
\");" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 13 "" 1 "" 
{GLPLOT2D 415 149 149 {PLOTDATA 2 "6'-%'CURVESG6$7S7$$!\"&\"\"!$\"#&*F
*7$$!1LLLe%G?y%!#:$\"1'HEiB]Jx)!#97$$!1mmT&esBf%F0$\"1LE:B[\"R;)F37$$!
1LL$3s%3zVF0$\"1>T+'y[X](F37$$!1ML$e/$QkTF0$\"1m01k!z$ooF37$$!1nmT5=q]
RF0$\"1EbhiTpiiF37$$!1LL3_>f_PF0$\"19b[)o?cs&F37$$!1++vo1YZNF0$\"1g%)R
EuK%>&F37$$!1LL3-OJNLF0$\"1jf5)[?9n%F37$$!1++v$*o%Q7$F0$\"1cu<#ekq<%F3
7$$!1mmm\"RFj!HF0$\"1dA$*GEb'p$F37$$!1LL$e4OZr#F0$\"1b%R$f?$oH$F37$$!1
+++v'\\!*\\#F0$\"1#GNMl%>tGF37$$!1+++DwZ#G#F0$\"1#p(e#G-fZ#F37$$!1+++D
.xt?F0$\"1#=b#Q^m>@F37$$!1LL3-TC%)=F0$\"1\"3/<R5)==F37$$!1mmm\"4z)e;F0
$\"19t*))e:\"*[\"F37$$!1mmmm`'zY\"F0$\"11l)>%GmL7F37$$!1++v=t)eC\"F0$
\"1#>m!3\\DS'*F07$$!1nmm;1J\\5F0$\"14[Tx2S+vF07$$!1$***\\(=[jL)!#;$\"1
Iq43.Q>aF07$$!1'***\\iXg#G'F[r$\"1rBmFa<(p$F07$$!1emmT&Q(RTF[r$\"1vuYs
%=+<#F07$$!1lm;/'=><#F[r$\"1C/OaVG55F07$$!1EMLLe*e$\\!#=$\"1Emj`sm\")>
!#<7$$\"1sm;zRQb@F[r$!1!=st)=$yA(F[r7$$\"1-+](=>Y2%F[r$!10dIH?xJ6F07$$
\"1vmm\"zXu9'F[r$!1hA#QiX_K\"F07$$\"1,+++&y))G)F[r$!1LrO'>'Qa7F07$$\"1
++]i_QQ5F0$!1uTo)*=4)=*F[r7$$\"1,+D\"y%3T7F0$!1p\"*[A#[YV$F[r7$$\"1++]
P![hY\"F0$\"1QI&f`!yTeF[r7$$\"1LLL$Qx$o;F0$\"1.7KY(Rpn\"F07$$\"1+++v.I
%)=F0$\"1Dan4Ac9JF07$$\"1mm\"zpe*z?F0$\"1:4Xj(\\)eYF07$$\"1,++D\\'QH#F
0$\"1xdV#=*)*4mF07$$\"1LLe9S8&\\#F0$\"1)))eQ>Xlp)F07$$\"1,+D1#=bq#F0$
\"1m]!oMTP6\"F37$$\"1LLL3s?6HF0$\"1aAiR`0y8F37$$\"1++DJXaEJF0$\"1%ym#*
Rm>o\"F37$$\"1ommm*RRL$F0$\"1NXtB2(4+#F37$$\"1om;a<.YNF0$\"1L3!)e'*)QN
#F37$$\"1NLe9tOcPF0$\"1qwy%pT0t#F37$$\"1,++]Qk\\RF0$\"1\\GbA%[+5$F37$$
\"1NL$3dg6<%F0$\"1o!pR#*46b$F37$$\"1ommmxGpVF0$\"1Kirpv[zRF37$$\"1++D
\"oK0e%F0$\"1%z*p?3<iWF37$$\"1,+v=5s#y%F0$\"19zX&pP#\\\\F37$$\"\"&F*$
\"#bF*-%'COLOURG6&%$RGBG$\"*++++\"!\")F*F*-F$6$7S7$F($!#MF*7$F.$!1+++v
q@pKF37$F5$!1++D^NUbJF37$F:$!1++]K3XFIF37$F?$!1++]F)H')*GF37$FD$!1++D'
3@/x#F37$FI$!1++Dr^b^EF37$FN$!1++D,kZGDF37$FS$!1++Dh\")=,CF37$FX$!1++D
O\"3VF#F37$Fgn$!1+++NkzV@F37$F\\o$!1++]d;%)G?F37$Fao$!1+++0)H%**=F37$F
fo$!1+++vl[p<F37$F[p$!1+++&>iUk\"F37$F`p$!1++DhkaI:F37$Fep$!1+++buK&R
\"F37$Fjp$!1+++?#z2G\"F37$F_q$!1++D\"RKv9\"F37$Fdq$!1+++qjeH5F37$Fiq$!
1'***\\7*3=+*F07$F_r$!1)***\\PFcpxF07$Fdr$!1&****\\7VQ['F07$Fir$!1****
\\i6:.`F07$F^s$!1,++v`hHSF07$Fes$!1(***\\7'pnq#F07$Fjs$!1****\\([G_b\"
F07$F_t$!1_****\\_K:JF[r7$Fdt$\"11+++5FL(*F[r7$Fit$\"1-++v:JIAF07$F^u$
\"1.+](o3lW$F07$Fcu$\"1+++D#))oz%F07$Fhu$\"1'******Hk-,'F07$F]v$\"1.++
]A!eI(F07$Fbv$\"1(***\\(=_(z%)F07$Fgv$\"12++]&*=j(*F07$F\\w$\"1++v3/3(
4\"F37$Faw$\"1++vB4JB7F37$Ffw$\"1+++DVsY8F37$F[x$\"1++v=n#fZ\"F37$F`x$
\"1,++!)RO+;F37$Fex$\"1,+]_!>ws\"F37$Fjx$\"1,+v)Q?Q&=F37$F_y$\"1,++5jy
p>F37$Fdy$\"1,+]Ujp-@F37$Fiy$\"1,++gEd@AF37$F^z$\"1++v3'>$[BF37$Fcz$\"
1,+D6EjpCF37$Fhz$\"#EF*-F][l6&F_[lF*F*F`[l-%&TITLEG6#Q@graphs~of~1st~&
~2nd~derivatives6\"-%+AXESLABELSG6$Q\"xF_elQ\"yF_el-%%VIEWG6$;F(FhzFhe
l" 1 2 0 1 2 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "solve(firstder = 0,x);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6$\"\"!#\"\"%\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "solve(secondder = 0, x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6##\"\"#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "   \+
" }{TEXT 273 5 "Value" }{TEXT 275 1 " " }{TEXT -1 60 "                \+
                                            " }{TEXT 274 11 "Conclusio
ns" }}{PARA 0 "" 0 "" {TEXT -1 100 "   f '(x) = 0  when x = 0 and x = \+
4/3                   Critical values: possible maximum or minimum" }}
{PARA 0 "" 0 "" {TEXT -1 40 "   f '(x) is defined for all values of x
" }}{PARA 0 "" 0 "" {TEXT -1 2 "  " }}{PARA 0 "" 0 "" {TEXT -1 106 " f
 '(x) < 0  when  0 < x < 4/3                            Graph of   f (
x)  is decreasing in this interval" }}{PARA 0 "" 0 "" {TEXT -1 106 " f
 '(x) > 0  when  x < 0 or  x > 4/3                    Graph of   f (x)
  is increasing in these intervals" }}{PARA 0 "" 0 "" {TEXT -1 88 " f \+
\"(x) = 0  when x = 2/3                                   Possible poi
nt of inflection" }}{PARA 0 "" 0 "" {TEXT -1 110 " f \"(x) < 0  when x
 < 2/3                                   Graph of   f (x)  is concave \+
down in this interval" }}{PARA 0 "" 0 "" {TEXT -1 108 " f \" (x) > 0 w
hen x > 2/3                                   Graph of   f (x)  is con
cave up in this interval" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Sketch:" }}
{PARA 13 "" 1 "" {GLPLOT2D 325 120 120 {PLOTDATA 2 "6%-%'CURVESG6$7S7$
$!\"&\"\"!$!$C#F*7$$!1LLLe%G?y%!#:$!1&>(*zOc#)*>!#87$$!1mmT&esBf%F0$!1
s]!)z:7-=F37$$!1LL$3s%3zVF0$!1C4Jx`!of\"F37$$!1ML$e/$QkTF0$!1DBiTV(eS
\"F37$$!1nmT5=q]RF0$!1cJ2+\"\\4B\"F37$$!1LL3_>f_PF0$!1p@6Ser\"3\"F37$$
!1++vo1YZNF0$!1NognY3)R*!#97$$!1LL3-OJNLF0$!1`ZZ^_.g!)FR7$$!1++v$*o%Q7
$F0$!1Mr;%e[<&oFR7$$!1mmm\"RFj!HF0$!1t#[(GWfLdFR7$$!1LL$e4OZr#F0$!1H_8
$)3i[[FR7$$!1+++v'\\!*\\#F0$!1?W7H&=)eRFR7$$!1+++DwZ#G#F0$!1:6`\\\\)H<
$FR7$$!1+++D.xt?F0$!1n.6<\"R?^#FR7$$!1LL3-TC%)=F0$!1%)\\X2y7*)>FR7$$!1
mmm\"4z)e;F0$!1q0PHbDd9FR7$$!1mmmm`'zY\"F0$!1,?7gSIy5FR7$$!1++v=t)eC\"
F0$!1vy@45&G9(F07$$!1nmm;1J\\5F0$!1U/LUubfXF07$$!1$***\\(=[jL)!#;$!1z@
rp+7fBF07$$!1'***\\iXg#G'F\\r$!1+P1FCEo#)F\\r7$$!1emmT&Q(RTF\\r$\"1fJ!
H\"4eNCF\\r7$$!1lm;/'=><#F\\r$\"1B')eDMl5!)F\\r7$$!1EMLLe*e$\\!#=$\"1d
svuU-****F\\r7$$\"1sm;zRQb@F\\r$\"10()[0-'=C)F\\r7$$\"1-+](=>Y2%F\\r$
\"1RNL=4[NSF\\r7$$\"1vmm\"zXu9'F\\r$!1D]UZ\"\\Kz#F\\r7$$\"1,+++&y))G)F
\\r$!1/eYt'G(y6F07$$\"1++]i_QQ5F0$!1i@%H=VL>#F07$$\"1,+D\"y%3T7F0$!1(e
j#zM`\\KF07$$\"1++]P![hY\"F0$!1&\\I?,VnW%F07$$\"1LLL$Qx$o;F0$!1(zcK8K+
\\&F07$$\"1+++v.I%)=F0$!1oHQ&\\x>^'F07$$\"1mm\"zpe*z?F0$!1rA^(zOlI(F07
$$\"1,++D\\'QH#F0$!1SxkP$pt(zF07$$\"1LLe9S8&\\#F0$!1,e4hZ$)o$)F07$$\"1
,+D1#=bq#F0$!1;*=)o]Qv%)F07$$\"1LLL3s?6HF0$!1,MIKwlF#)F07$$\"1++DJXaEJ
F0$!1d`7\"Rs#QvF07$$\"1ommm*RRL$F0$!1Dz$p(4O.kF07$$\"1om;a<.YNF0$!1L7y
<;N3ZF07$$\"1NLe9tOcPF0$!1X(G3;HxV#F07$$\"1,++]Qk\\RF0$\"1\"**faW)fW@F
\\r7$$\"1NL$3dg6<%F0$\"1ALQr4&z(RF07$$\"1ommmxGpVF0$\"1W$H?&H&*\\!)F07
$$\"1++D\"oK0e%F0$\"1(pyF&=.=8FR7$$\"1,+v=5s#y%F0$\"1#)RVf*G/*=FR7$$\"
\"&F*$\"#EF*-%'COLOURG6&%$RGBG$\"#5!\"\"F*F*-%+AXESLABELSG6$Q\"x6\"Q\"
yFg[l-%%VIEWG6$;F(Fhz;$!#5F*$Fa[lF*" 1 2 0 1 2 2 9 1 4 2 1.000000 
46.000000 37.000000 0 }}}}}{PARA 0 "" 0 "" {TEXT -1 76 "______________
______________________________________________________________" }}
{PARA 258 "" 0 "" {TEXT -1 0 "" }{TEXT 269 9 "ASSIGNMEN" }{TEXT 268 1 
"T" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 270 10 "Problem 1:" }}
{PARA 0 "" 0 "" {TEXT -1 15 "Given f '(x) = " }{XPPEDIT 18 0 "3*x^2;" 
"6#*&\"\"$\"\"\"*$%\"xG\"\"#F%" }{TEXT -1 20 "  and  f (0) = -3,  " }}
{PARA 0 "" 0 "" {TEXT -1 16 " a) find  f \"(x)" }}{PARA 0 "" 0 "" 
{TEXT -1 55 " b) plot  f '(x)  and  f \"(x)  on the same set of axes.
" }}{PARA 0 "" 0 "" {TEXT -1 45 " c) determine where:  f '(x) = 0,  f \+
\"(x) = 0" }}{PARA 0 "" 0 "" {TEXT -1 90 " d) determine the intervals \+
for which:   f '(x) >0,  f '(x) < 0,  f \"(x) < 0,  f \"(x) > 0 " }}
{PARA 0 "" 0 "" {TEXT -1 80 " e) organize the data in a table and draw
 conclusions about the graph of  f (x)." }}{PARA 0 "" 0 "" {TEXT -1 
50 " f)  hand sketch  f (x)  using the initial value. " }}}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 5 "
" 0 "" {TEXT -1 0 "" }{TEXT 271 10 "Problem 2:" }{TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 42 "Given f '(x) =  -sin x   and  f (0) = 2, \+
 " }}{PARA 0 "" 0 "" {TEXT -1 16 " a) find  f \"(x)" }}{PARA 0 "" 0 "
" {TEXT -1 55 " b) plot  f '(x)  and  f \"(x)  on the same set of axes
." }}{PARA 0 "" 0 "" {TEXT -1 45 " c) determine where:  f '(x) = 0,  f
 \"(x) = 0" }}{PARA 0 "" 0 "" {TEXT -1 90 " d) determine the intervals
 for which:   f '(x) >0,  f '(x) < 0,  f \"(x) < 0,  f \"(x) > 0 " }}
{PARA 0 "" 0 "" {TEXT -1 81 " e) organize the data in a table and draw
 conclusions about the graph of   f (x)." }}{PARA 0 "" 0 "" {TEXT -1 
49 " f)  hand sketch  f (x)  using the initial value." }}}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 272 
10 "Problem 3:" }}{PARA 0 "" 0 "" {TEXT -1 106 "Given f '(x) < 0 when \+
x < -2 ,  f '(x) > 0 when x > -2,   f \"(x) > 0 for all x , and  f (x)
 > 0 for all x," }}{PARA 0 "" 0 "" {TEXT -1 19 "a) plot  f (x) =   " }
{XPPEDIT 18 0 "x^6+4;" "6#,&*$%\"xG\"\"'\"\"\"\"\"%F'" }{TEXT -1 69 " \+
 and discuss whether or not the graph would meet the given criteria." 
}}{PARA 0 "" 0 "" {TEXT -1 90 "b) determine the equation of another fu
nction which would also meet the given criteria.   " }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 71 "_______________
________________________________________________________" }}{PARA 0 "
" 0 "" {TEXT -1 94 "MSIP Grant #P120A80089-98: \"Three Urban Calculus \+
Reform Programs: Adopting the Best\" 1998-2001" }}}}{MARK "16 2 0" 16 
}{VIEWOPTS 0 0 0 1 1 1803 }