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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 102 " MAXIMUM AND MINIMUM VALUES  \n\nWe look for the \+
critical points of several functions\nof two variables.\n" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 "First function. This func
tion has one critical point,\na local minimum." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "f:=x^2+y^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG
,&*$%\"xG\"\"#\"\"\"*$%\"yGF(F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 36 "plot3d(f,x=-2..2,y=-2..2,color=red);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 41 "contourplot(f,x=-2..2,y=-2..2,color=red);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 50 "Second function: This function has a saddle point." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "g:=x^2-y^2;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"gG,&*$%\"xG\"\"#\"\"\"*$%\"yGF(!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot3d(g,x=-2..2,y=-2..2,color=red)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "contourplot(g,x=-2..2,
y=-2..2,color=red);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "Third function. This function has \+
local maximum and\nlocal minima.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
19 "h:=(x^2-4)^2+6*y^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG,&*$,
&*$%\"xG\"\"#\"\"\"!\"%F+F*F+*$%\"yGF*\"\"'" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 36 "plot3d(h,x=-3..3,y=-2..2,color=red);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "contourplot(h,x=-3..3,y=-2..2,color
=red);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 127 "Fourth function. We look at this function on a
 limited domain.\nIt achieves its absolute maximum on the boundary of \+
the domain.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "q:=x^2+2*x*y-y;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG,(*$%\"xG\"\"#\"\"\"*&F'F)%\"yG
F)F(F+!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot3d(q,x=-
2..2,y=-2..2,color=red);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 
"contourplot(q,x=-2..2,y=-2..2,color=red);" }}}{EXCHG {PARA 0 "> " 0 "
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