{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 "Times" 1 12 0 0 0 1 2 2 2 2 
2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 
11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 
0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "
Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }
}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "z:=4*x^2+3*x*(57-x)+
6*(57.0-x)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG,(*$)%\"xG\"\"#
\"\"\"\"\"%*(\"\"$F*F(F*,&\"#dF*F(!\"\"F*F**&\"\"'F*),&$\"$q&F0F*F(F0F
)F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "z1:=diff(z,x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#z1G,&%\"xG\"#9$\"%I^!\"\"F*" }}}
{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "solve(z1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+9
dGkO!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eval(z,x=36.6);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"(7&45!\"#" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 33 "z:=4*x^2+3*x*(56-x)+6*(56.0-x)^2;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"zG,(*$)%\"xG\"\"#\"\"\"\"\"%*(\"\"$F*F(F
*,&\"#cF*F(!\"\"F*F**&\"\"'F*),&$\"$g&F0F*F(F0F)F*F*" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 14 "z1:=diff(z,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#z1G,&%\"xG\"#9$\"%S]!\"\"F*" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 12 "solve(z1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
$\"#O\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "eval(z,x=36);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"'+W(*!\"#" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 15 "z2:=diff(z1,x);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#z2G\"#9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot(z,
x=-100..100);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6
%-%'CURVESG6$7S7$$!$+\"\"\"!$\"';#R\"F*7$$!3cmmm;p0k&*!#;$\"3]wm`hn[58
!#77$$!3#QLL3<XZ=*F0$\"3mB?ejzeT7F37$$!3WmmmT%p\"e()F0$\"3k1Ekj/^m6F37
$$!3pmmm\"4m(G$)F0$\"3+vyGB#3N4\"F37$$!3sLL$3i.9!zF0$\"3tE_u'*fTB5F37$
$!3wmm;/R=0vF0$\"3(yOv\"ow:2'*!#87$$!3%*****\\P8#\\4(F0$\"37&*=2pR4\")
*)FM7$$!3]mm;/siqmF0$\"3O)y(o@[Se$)FM7$$!3u****\\(y$pZiF0$\"33GcE0^zix
FM7$$!3jKLL$yaE\"eF0$\"3U]X\"\\!\\EwrFM7$$!3+mmm\">s%HaF0$\"3%Rr0Uw&f
\"o'FM7$$!3'*)*****\\$*4)*\\F0$\"3!p#HFq=J\\hFM7$$!3))******\\_&\\c%F0
$\"3bz^T'fa5k&FM7$$!37******\\1aZTF0$\"3Uo\"Q'Gq5w^FM7$$!37mm;/#)[oPF0
$\"3uKg/*GB]x%FM7$$!31KLL$=exJ$F0$\"3rp_\")zkFCVFM7$$!3PLLLL2$f$HF0$\"
3u$=l&QtokRFM7$$!3I****\\PYx\"\\#F0$\"3'y<'Qw-3sNFM7$$!3sKLLL7i)4#F0$
\"3YD)ps()*fZKFM7$$!3o)***\\P'psm\"F0$\"3;b!*Qg!*[;HFM7$$!3c****\\74_c
7F0$\"31)[[hn0ai#FM7$$!3))=LL$3x%z#)!#<$\"3-39aj/(oM#FM7$$!3JELL3s$QM%
Ffr$\"3B]Z[Swt8@FM7$$!3o&ylmm\"zr)*!#>$\"3?\\*eY?#e')=FM7$$\"3fVLLezw5
VFfr$\"3'\\Tt\"*>Xtn\"FM7$$\"395++v$Q#\\\")Ffr$\"3U+[;YaO<:FM7$$\"3)QL
L$e\"*[H7F0$\"3SW@`:Dvn8FM7$$\"3a++++dxd;F0$\"3DMd?mkXQ7FM7$$\"3g+++D0
xw?F0$\"3@9cMif\"o8\"FM7$$\"3Q++]i&p@[#F0$\"3#35!4U\"o=1\"FM7$$\"3H***
**\\2'HKHF0$\"3eGA?(*zg05FM7$$\"3pmmmmZvOLF0$\"3%Q!4,P'3Dz*!#97$$\"3m,
++]2goPF0$\"3Y%RI!\\$)*Qw*F\\v7$$\"3UKL$eR<*fTF0$\"3CZ(4JCbM'**F\\v7$$
\"3M-++])Hxe%F0$\"30s1'zr#pU5FM7$$\"3alm;H!o-*\\F0$\"3`2Y]j\"*p46FM7$$
\"3!=++DTO5T&F0$\"3Oh!=@q*)R?\"FM7$$\"3<mmm;WTAeF0$\"3m[&e(3)Q,K\"FM7$
$\"3A,+]i!*3`iF0$\"3U***[,r@rY\"FM7$$\"3!fLLL$*zym'F0$\"3%\\Xu*4@BL;FM
7$$\"3uLLL3N1#4(F0$\"35KjBGb,G=FM7$$\"3spm;HYt7vF0$\"3u-'z%fW1Y?FM7$$
\"39-+++xG**yF0$\"31#*f\"4Br#oAFM7$$\"3[nmmT6KU$)F0$\"370*[nos'[DFM7$$
\"3*\\LLL`v&Q()F0$\"3RPS#e4ZF#GFM7$$\"3i-+]i`1h\"*F0$\"3I5)>wN\"=RJFM7
$$\"3%H++v.Uac*F0$\"3u_S>4\\XlMFM7$$\"$+\"F*$\"&;%QF*-%'COLOURG6&%$RGB
G$\"#5!\"\"$F*F*Fd[l-%+AXESLABELSG6$Q\"x6\"Q!6\"-%%VIEWG6$;F(Fiz%(DEFA
ULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1
" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 95 "What happens to the z functi
on, if we change the constrait by one unit: i.e. x+y =57 or x+y=55." }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 33 "z:=4*x^2+3*x*(57-x)+6*(57.0-x)^2;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"zG,(*$)%\"xG\"\"#\"\"\"\"\"%*(\"\"$F*F(F*,&\"#dF*F(!\"\"F*F*
*&\"\"'F*),&$\"$q&F0F*F(F0F)F*F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "z1:=diff(z,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#
z1G,&%\"xG\"#9$\"%I^!\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "solve(z1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+9dGkO!\")" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "eval(z,x=36.64285714);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+92^45!\"&" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 31 "changeinz:=10095.10714-9744.00;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%*changeinzG$\")926N!\"&" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 33 "z:=4*x^2+3*x*(55-x)+6*(55.0-x)^2;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"zG,(*$)%\"xG\"\"#\"\"\"\"\"%*(\"\"$F*F(F*,&
\"#bF*F(!\"\"F*F**&\"\"'F*),&$\"$]&F0F*F(F0F)F*F*" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 14 "z1:=diff(z,x);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#z1G,&%\"xG\"#9$\"%]\\!\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "solve(z1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+'
G9d`$!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "eval(z,x=35.35
714286);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Ur5*R*!\"'" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "changeinz:=9744.00-9399.107142;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*changeinzG$\"*eG*[M!\"'" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "z:=4*x^2+3*x*y+6*y^2 +lambda*(56-x-
y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG,**$)%\"xG\"\"#\"\"\"\"\"
%*(\"\"$F*F(F*%\"yGF*F**&\"\"'F*)F.F)F*F**&%'lambdaGF*,(\"#cF*F(!\"\"F
.F6F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "zx:=diff(z,x);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#zxG,(%\"xG\"\")*&\"\"$\"\"\"%\"yG
F*F*%'lambdaG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "zy:=d
iff(z,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#zyG,(%\"xG\"\"$*&\"#7
\"\"\"%\"yGF*F*%'lambdaG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 19 "zl:=diff(z,lambda);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#zlG,(
\"#c\"\"\"%\"xG!\"\"%\"yGF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
31 "solve(\{zx,zy,zl\},\{x,y,lambda\});" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#<%/%'lambdaG\"$[$/%\"yG\"#?/%\"xG\"#O" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 31 "z:=48*y-3*x^2-6*x*y-2*y^2+72*x;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"zG,,%\"yG\"#[*&\"\"$\"\"\")%\"xG\"\"#F*!\"\"*(\"
\"'F*F,F*F&F*F.*&F-F*)F&F-F*F.*&\"#sF*F,F*F*" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 31 "z:=48*y-3*x^2-6*x*y-2*y^2+72*x;" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%\"zG,,%\"yG\"#[*&\"\"$\"\"\")%\"xG\"\"#F*!\"\"*(\"\"'F*F,F*F&F*F.
*&F-F*)F&F-F*F.*&\"#sF*F,F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 14 "zx:=diff(z,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#zxG,(%\"xG!
\"'*&\"\"'\"\"\"%\"yGF*!\"\"\"#sF*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "zxx:=diff(zx,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%$zxxG!\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "zy:=diff(z,y)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#zyG,(\"#[\"\"\"*&\"\"'F'%\"xGF
'!\"\"*&\"\"%F'%\"yGF'F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 
"zyy:=diff(zy,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$zyyG!\"%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "zxy:=diff(zx,y);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$zxyG!\"'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "zyx:=diff(zy,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%$zyxG!\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "pofseder:=zxx
*zyy;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)pofsederG\"#C" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "szyx:=(zyx)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%
szyxG\"#O" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 116 "Since zxx*zyy=24 an
d is less than squared of the partials:36, that is zxx*zyy<(zxy)^2, we
 an inlection  point--ie an" }}{PARA 0 "" 0 "" {TEXT -1 115 "inflecion
 point, where a minimum is crossing over a maximum. The added conditio
n for a saddle point is for zxx and " }}{PARA 0 "" 0 "" {TEXT -1 28 "z
yy to have different signs." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "z:=5*x^2-3*y
^2-30*x+7*y+4*x*y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG,,*$)%\"xG
\"\"#\"\"\"\"\"&*&\"\"$F*)%\"yGF)F*!\"\"*&\"#IF*F(F*F0*&\"\"(F*F/F*F**
(\"\"%F*F(F*F/F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot3
d(z,x=-15..15,y=-10..10);" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 
{PLOTDATA 3 "6$-%%GRIDG6%;$!#:\"\"!$\"#:F);$!#5F)$\"#5F)X,%)anythingG6
\"6\"][[[[]\\q\\bm\":\":409C340000000000409C430000000000409C4155555555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-%+AXESLABELSG6%%\"xG%\"yGQ!6\"" 1 2 0 1 10 0 2 1 1 1 2 
1.000000 -77.000000 -24.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 14 "zx:=diff(z,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%#zxG,(%\"xG\"#5\"#I!\"\"*&\"\"%\"\"\"%\"yGF,F," }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 16 "zxx:=diff(zx,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$zxxG\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
14 "zy:=diff(z,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#zyG,(%\"yG!\"
'\"\"(\"\"\"*&\"\"%F)%\"xGF)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 16 "zyy:=diff(zy,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$zyyG!\"
'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "zxy:=diff(zx,y);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$zxyG\"\"%" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 16 "zyx:=diff(zy,x);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$zyxG\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "zxx*zy
y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!#g" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 6 "zxy^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#;" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 249 "since the product of the second d
erivative is -60 and is less than the squared partials, we neither hav
e a maximum or a minimum. Since the second partial with respect to x i
s 10 and the second partial with respect to y is -6, we have a saddle \+
point." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "z:=3*x^3-5*y^2-225*x+70*y+23
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG,,*$)%\"xG\"\"$\"\"\"F)*&\"
\"&F*)%\"yG\"\"#F*!\"\"*&\"$D#F*F(F*F0*&\"#qF*F.F*F*\"#BF*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "zx:=diff(z,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#zxG,&*$)%\"xG\"\"#\"\"\"\"\"*\"$D#!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "solve(zx,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"\"&!\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "
5., -5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "zy:=diff(z,y);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#zyG,&%\"yG!#5\"#q\"\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "solve(zy,y);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
16 "zyy:=diff(zy,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$zyyG!#5" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "zxy:=diff(zx,y);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$zxyG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "zxx:=diff(zx,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%$zxxG,$%\"xG\"#=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eval(z
xx,x=5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#!*" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 14 "eval(zyy,y=7);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "90*(-10);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#!$+*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "-900<0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#2!$+*\"\"!
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "we have a saddle point at x=5
, y=7." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eval(zxx,x=-5);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#!#!*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "-90*(-10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$+*" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "900>0;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#2\"\"!\"$+*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 116 "
Since the product of the second derivatioves is greater than squared c
ross partials, and both second derivatives are" }}{PARA 0 "" 0 "" 
{TEXT -1 28 "negative, we have a maximum." }}}}{MARK "70 1 0" 28 }
{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }