{VERSION 6 0 "IBM INTEL LINUX" "6.0" }
{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 "" 0 1 0 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 "Maple Output" 0 11 1 
{CSTYLE "" -1 -1 "" 0 1 0 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 "" 0 256 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 
1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 
-1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 46 "Tool til bestemmelse af \+
kritiske punkters art." }}{PARA 258 "" 0 "" {TEXT -1 32 "Al anvendelse
 er p\345 eget ansvar." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 41 "Vejledning:\n1) Udfyld v\346rdier for opgaven" }}
{PARA 0 "" 0 "" {TEXT -1 54 "2) G\345 til bunden af maple-arket og try
k \"!!!\"-knappen\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "with
(RealDomain):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 
0 "" {TEXT -1 56 "--- Skriv forskriften for funktionen, du vil unders
\370ge. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "f:=x^3* y^2 * e
xp(-(3*x^2+y^4)/2);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"fG*()%\"xG\"\"$\"\"\")%\"yG\"\"#F)-%$expG6#
,&*(F(F)F,!\"\"F'F,F2*&F,F2F+\"\"%F2F)" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 17 "1. ordens afledte" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 24 "f1:=simplify(diff(f,x));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#f1G,$*,\"\"$\"\"\")%\"xG\"\"#F()%\"yGF+F(-%$expG6#
,&*(F'F(F+!\"\"F*F+F3*&F+F3F-\"\"%F3F(,&F(F3*$F)F(F(F(F3" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f2:=simplify(diff(f,y));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#f2G,$*,\"\"#\"\"\")%\"xG\"\"$F(%\"yGF(-%$
expG6#,&*(F+F(F'!\"\"F*F'F2*&F'F2F,\"\"%F2F(,&F(F2*$)F,F4F(F(F(F2" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "2. ordens afledte" }{MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "f11:=simplify(diff(f
,x,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$f11G,$*,\"\"$\"\"\"%\"xG
F()%\"yG\"\"#F(-%$expG6#,&*(F'F(F,!\"\"F)F,F2*&F,F2F+\"\"%F2F(,(F,F(*&
\"\"(F()F)F,F(F2*&F'F()F)F4F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "f12:=simplify(diff(f,x,y));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$f12G,$*,\"\"'\"\"\")%\"xG\"\"#F(%\"yGF(-%$expG6#,&*(
\"\"$F(F+!\"\"F*F+F3*&F+F3F,\"\"%F3F(,*F(F(*$)F,F5F(F3*$F)F(F3*&F)F(F8
F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "f22:=simplify(d
iff(f,y,y));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$f22G,$**\"\"#\"\"\"
)%\"xG\"\"$F(-%$expG6#,&*(F+F(F'!\"\"F*F'F1*&F'F1%\"yG\"\"%F1F(,(F(F(*
&\"\"(F()F3F4F(F1*&F'F()F3\"\")F(F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 17 "Punkter hvor f1=0" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 27 "points1:=solve(f1=0,\{x,y\});" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%(points1G6(<$/%\"yGF(/%\"xG\"\"!F&<$/F(F+/F*F*
F,<$F'/F*\"\"\"<$F'/F*!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Pu
nkter hvor f2=0" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "points2:=solve(f2=0,\{x,y\});" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%(points2G6(<$/%\"yGF(/%\"xG\"\"!F&F&<$/F(F+/F*F*<$F./
F(\"\"\"<$F./F(!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Punkter h
vor f1=f2=0" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 35 "points:=[op(\{solve([f1=0,f2=0])\})];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'pointsG7(<$/%\"yG\"\"!/%\"xGF+<$/F(F(/F+F)<$/F+\"\"
\"/F(F1<$F2/F+!\"\"<$/F(F5F4<$F0F7" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "A:=[seq
(simplify(subs(i[1],i[2],f11)),i in points)]:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 52 "B:=[seq(simplify(subs(i[1],i[2],f12)),i in point
s)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "C:=[seq(simplify(su
bs(i[1],i[2],f22)),i in points)]:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 231 "pointt
ype:= proc(A,B,C)\n  if (is((A*C-B^2) > 0 and A > 0)) then \"Lokalt mi
nimum\"\n  elif (is((A*C-B^2) > 0 and A < 0)) then \"Lokalt maksimum\"
\n  elif (is((A*C-B^2) < 0)) then \"Saddelpunkt\"\n  else \"Ingen konk
lusion\"\n  end if\nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 270 "pointtable := [\n
  seq([\n  cat(\"(\", convert(op(2,op(select(has,points[i],x))),string
), \",\", convert(op(2,op(select(has,points[i],y))),string), \")\"),\n
  A[i],\n  B[i],\n\n  C[i],\n  A[i]*C[i]-B[i]^2,\n  pointtype(A[i], B[
i], C[i]),\n  subs(points[i], f)  \n]\n  ,i=1..nops(A))  \n]:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "with(Maplets[Elements]):" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "maplet1:=Maplet([\n  BoxCe
ll(Table([\"(a,b)\", \"A=f11\",\"B=f12\",\"C=f22\",\"AC-B^2\",\"Type\"
,\"f(a,b)\"],pointtable), 'as_needed'),\n  Button(\"OK\",Shutdown())\n
]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "Maplets[Display](map
let1);" }}}{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 "28 0 0" 0 }{VIEWOPTS 1 1 0 1 
1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }