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1 "" {XPPMATH 20 "6#>%&guessG7$$\"\")!\"\"$\"#;F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&guessG7$$\"#k!\"#$\"$G\"F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&guessG7$$\"$7&!\"$$\"%C5F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&guessG7$$\"%'4%!\"%$\"%#>)F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&guessG7$$\"&oF$!\"&$\"&Ob'F(" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 75 "guess:=[1,2];\nfor i from 1 to 10 do\n  guess \+
:= gradstep2(f,guess,.25);\nod;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%&guessG7$\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$
\"#]!\"#$\"$+\"F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$\"%+D
!\"%$\"%+]F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$\"'+]7!\"'
$\"'++DF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$\"(++D'!\")$
\")++]7F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$\"*++]7$!#5$
\"*+++D'F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$\"+++]i:!#6$
\"++++DJF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$\"+++]7y!#7$
\"+++]i:!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$\"+++D1R!#7
$\"+++]7yF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$\"++]7`>!#7
$\"+++D1RF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$\"++]il(*!#
8$\"++]7`>!#7" }}}{EXCHG {PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"!F$" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "guess:=[1,2];\nfor i from 1
 to 10 do\n  guess := gradstep2(f,guess,.5);\nod;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&guessG7$\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%&guessG7$\"\"!F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$\"
\"!F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$\"\"!F&" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$\"\"!F&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&guessG7$\"\"!F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%&guessG7$\"\"!F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$\"\"!F
&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$\"\"!F&" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%&guessG7$\"\"!F&" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%&guessG7$\"\"!F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
118 "findMin:= proc(f,guess)\n  local i, h;\n  h:=.1;\n  for i from 1 \+
to 10 do\n     guess := gradstep2(f,guess,h);\n  od;\n end;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%(findMinGR6$%\"fG%&guessG6$%\"iG%\"hG6\"F,
C$>8%$\"\"\"!\"\"?(8$F1F1\"#5%%trueG>9%-%*gradstep2G6%9$F8F/F,F,F," }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "findMin(f,[1,2]);" }}{PARA 
8 "" 1 "" {TEXT -1 53 "Error, (in findMin) illegal use of a formal par
ameter" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 153 "findMin:= proc(f
,firstguess)\n  local i, h, guess;\n  guess := firstguess;\n  h:=.1;\n
  for i from 1 to 10 do\n     guess := gradstep2(f,guess,h);\n  od;\n \+
end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(findMinGR6$%\"fG%+firstgues
sG6%%\"iG%\"hG%&guessG6\"F-C%>8&9%>8%$\"\"\"!\"\"?(8$F5F5\"#5%%trueG>F
0-%*gradstep2G6%9$F0F3F-F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 17 "findMin(f,[1,2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+C=ut5
!#5$\"+[O[Z@F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "findMin:
= proc(f,firstguess)\n  local i, h, guess;\n  guess := firstguess;\n  \+
h:=.1;\n  for i from 1 to 100 do\n     guess := gradstep2(f,guess,h);
\n  od;\n end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(findMinGR6$%\"fG%
+firstguessG6%%\"iG%\"hG%&guessG6\"F-C%>8&9%>8%$\"\"\"!\"\"?(8$F5F5\"$
+\"%%trueG>F0-%*gradstep2G6%9$F0F3F-F-F-" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "findMin(f,[1,2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
7$$\"+xf.P?!#>$\"+]>2uSF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
23 "g:=(x,y)->abs(x + y^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGR
6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF)-%$absG6#,&9$\"\"\"*$)9%\"\"#\"
\"\"F2F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "findMin(g,[
1,2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"!$\"+5/'3U$!#6" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "op([a,b]);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6$%\"aG%\"bG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 22 "op([ [a,b], [c,d,e]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$7$%\"a
G%\"bG7%%\"cG%\"dG%\"eG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 342 
"findMin:= proc(f,firstguess)\n  local i, h, guess, oldht, ht;\n  gues
s := firstguess;\n  oldht := f(op(guess));\n  h:=.1;\n  for i from 1 t
o 100 do\n     guess := gradstep2(f,guess,h);\n     ht := f(op(guess))
;\nprint(i,guess,ht);\n     if ( abs(oldht - ht) < .00001) then\n     \+
   RETURN(guess);\n     fi;\n     oldht := ht;\n  od;\n  RETURN(guess)
;\n end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "findMin(f,[1,2]
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!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"#7$$\"#k!\"#$\"$G\"F'$\"&!
[?!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"$7$$\"$7&!\"$$\"%C5F'$\"
(?2J\"!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%7$$\"%'4%!\"%$\"%#>
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&$\"&Ob'F'$\"+?\"4(o`!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"'7$$\"
'W@E!\"'$\"')GC&F'$\"+OQ(fV$!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"
\"(7$$\"(_r4#!\"($\"(/V>%F'$\"+bK-*>#!#5" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6%\"\")7$$\");sx;!\")$\")KWbLF'$\"+%)[P29!#5" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6%\"\"*7$$\"*Gx@M\"!\"*$\"*caVo#F'$\"+b#*>2!*!#6" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#57$$\"+C=ut5!#5$\"+[O[Z@F'$\"+Bvgkd
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!#5$\"+8)[$*o$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#77$$\"+uw%>(o!#
6$\"+M&*Qu8!#5$\"+RK=hBF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#87$$\"
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"6%\"#97$$\"+6l/)R%!#6$\"+;I4'z)F'$\"+YlSr'*!#7" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6%\"#:7$$\"+4sV=N!#6$\"+8W(o.(F'$\"+*=+(*='!#7" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6%\"#;7$$\"+n(\\Z\"G!#6$\"+I&*\\HcF'$\"+@\"39'
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'$\"+(>,``#!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#=7$$\"+^)R9!=!#6$
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%\"#?7$$\"+0:#H:\"!#6$\"+2I%eI#F'$\"+q*Rhk'!#8" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6%\"#@7$$\"+S?PB#*!#7$\"+1WnW=!#6$\"+#eHND%!#8" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6%\"#A7$$\"+Kwpyt!#7$\"+D&RdZ\"!#6$\"+L*eAs#!#
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6$\"+<dCU<!#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#C7$$\"+&[mBs%!#7$
\"+gHtW%*F'$\"+fs.:6!#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#D7$$\"+)
=$*yx$!#7$\"+ojybvF'$\"+e%Qi8(!#9" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%
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{XPPMATH 20 "6%\"#F7$$\"+S;&yT#!#7$\"+vKqN[F'$\"+rK+BH!#9" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6%\"#G7$$\"+78GM>!#7$\"+?EcoQF'$\"+$4A2(=!#9" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#H7$$\"+]]UZ:!#7$\"+'4][4$F'$\"+S@E(
>\"!#9" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+]]UZ:!#7$\"+'4][4$F&" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "25 0 0" 0 }
{VIEWOPTS 1 1 0 2 1 1805 }