{VERSION 5 0 "IBM INTEL LINUX" "5.0" }
{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 }
{CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 0 0 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 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 "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 70 "5-Point Fo
rmula for the Derivative using Lagrange Polynomials in Maple" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "L
[0]:=( (x-b)*(x-c)*(x-d)*(x-e) )/( (a-b)*(a-c)*(a-d)*(a-e) );" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"LG6#\"\"!*2,&%\"xG\"\"\"%\"bG!\"
\"F+,&F*F+%\"cGF-F+,&F*F+%\"dGF-F+,&F*F+%\"eGF-F+,&%\"aGF+F,F-F-,&F5F+
F/F-F-,&F5F+F1F-F-,&F5F+F3F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 62 "L[1]:=( (x-a)*(x-c)*(x-d)*(x-e) )/( (b-a)*(b-c)*(b-d)*(b-e) );
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"LG6#\"\"\"*2,&%\"xGF'%\"aG!\"
\"F',&F*F'%\"cGF,F',&F*F'%\"dGF,F',&F*F'%\"eGF,F',&%\"bGF'F+F,F,,&F4F'
F.F,F,,&F4F'F0F,F,,&F4F'F2F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 62 "L[2]:=( (x-a)*(x-b)*(x-d)*(x-e) )/( (c-a)*(c-b)*(c-d)*(c-e) );
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"LG6#\"\"#*2,&%\"xG\"\"\"%\"aG
!\"\"F+,&F*F+%\"bGF-F+,&F*F+%\"dGF-F+,&F*F+%\"eGF-F+,&%\"cGF+F,F-F-,&F
5F+F/F-F-,&F5F+F1F-F-,&F5F+F3F-F-" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 62 "L[3]:=( (x-a)*(x-b)*(x-c)*(x-e) )/( (d-a)*(d-b)*(d-c)
*(d-e) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"LG6#\"\"$*2,&%\"xG\"
\"\"%\"aG!\"\"F+,&F*F+%\"bGF-F+,&F*F+%\"cGF-F+,&F*F+%\"eGF-F+,&%\"dGF+
F,F-F-,&F5F+F/F-F-,&F5F+F1F-F-,&F5F+F3F-F-" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 62 "L[4]:=( (x-a)*(x-b)*(x-c)*(x-d) )/( (e-a)*(e-b)*(e-
c)*(e-d) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"LG6#\"\"%*2,&%\"xG
\"\"\"%\"aG!\"\"F+,&F*F+%\"bGF-F+,&F*F+%\"cGF-F+,&F*F+%\"dGF-F+,&%\"eG
F+F,F-F-,&F5F+F/F-F-,&F5F+F1F-F-,&F5F+F3F-F-" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 90 "f:=y[0]*L[0]+y[1]*L[1]+y[2]*L[2]+y[3]*L[3]+y[4]*
L[4]+(C/5!)*(x-a)*(x-b)*(x-c)*(x-d)*(x-e);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%\"fG,.*4&%\"yG6#\"\"!\"\"\",&%\"xGF+%\"bG!\"\"F+,&F-F
+%\"cGF/F+,&F-F+%\"dGF/F+,&F-F+%\"eGF/F+,&%\"aGF+F.F/F/,&F7F+F1F/F/,&F
7F+F3F/F/,&F7F+F5F/F/F+*4&F(6#F+F+,&F-F+F7F/F+F0F+F2F+F4F+,&F.F+F7F/F/
,&F.F+F1F/F/,&F.F+F3F/F/,&F.F+F5F/F/F+*4&F(6#\"\"#F+F>F+F,F+F2F+F4F+,&
F1F+F7F/F/,&F1F+F.F/F/,&F1F+F3F/F/,&F1F+F5F/F/F+*4&F(6#\"\"$F+F>F+F,F+
F0F+F4F+,&F3F+F7F/F/,&F3F+F.F/F/,&F3F+F1F/F/,&F3F+F5F/F/F+*4&F(6#\"\"%
F+F>F+F,F+F0F+F2F+,&F5F+F7F/F/,&F5F+F.F/F/,&F5F+F1F/F/,&F5F+F3F/F/F+*0
\"$?\"F/%\"CGF+F>F+F,F+F0F+F2F+F4F+F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "df:=simplify(diff(f,x)):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 18 "df1:=subs(x=c,df):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "df2:=simplify(subs(\{a=c-2*h,b=c-h,d=c+h,e=c+2*h\},df
1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$df2G,$*&#\"\"\"\"#gF(*&%\"h
G!\"\",,*(\"\"#F(%\"CGF()F+\"\"&F(F(*&F2F(&%\"yG6#\"\"!F(F(*&F2F(&F56#
\"\"%F(F,*&\"#SF(&F56#\"\"$F(F(*&F=F(&F56#F(F(F,F(F(F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 1 0" 0 }{VIEWOPTS 1 
1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }