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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 191 "Given the following (arbi
trary) two functions. We want to show that for all points on y=f(x), t
here is a point on y=g(x) (say c) so that the distance is the shortest
 between these two curves." }}{PARA 0 "" 0 "" {TEXT -1 159 "Key: If we
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{MPLTEXT 1 0 16 "g:=x->-cos(x-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "fsolve(f(x)-g(x)=0);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'fsolveG6$/,(-%$sinG6#%\"xG\"\"\"\"
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{MPLTEXT 1 0 23 "subs(x=c,diff(g(x),x));" }}{PARA 11 "" 1 "" {XPPMATH 
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{MPLTEXT 1 0 52 "eq1:=((g(c)-f(x))/(c-x))*subs(x=c,diff(g(x),x))+1=0;
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "x1:=-1.030769192;" }}{PARA 
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>%#y1G$\"+q_IUT!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "eq3:
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{XPPMATH 20 "6#>%$eq3G/,&*(,&-%$cosG6#,&%\"cG\"\"\"F.!\"\"F/$\"+q_IUT!
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{XPPMATH 20 "6#>%#c1G$\"+Nr-S:!\"*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6 "g(c1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!++t%pd)!#5
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "with(linalg):with(plots
):with(student):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protecte
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7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefin
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