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{SECT 0 {EXCHG {PARA 19 "" 0 "" {TEXT -1 16 "Dr. Wei-Chi Yang" }}
{PARA 19 "" 0 "" {TEXT -1 18 "Radford University" }}{PARA 19 "" 0 "" 
{TEXT -1 21 "www.radford.edu/wyang" }}{PARA 0 "" 0 "" {TEXT -1 124 "Le
t f(x,y,z)=x^2+y^2+z^2 and g(x,y,z)=x^2+y^2/4+z^2/9. Discuss the extre
mum (max or min) for f(x,y,z) subject to g(x,y,z)=1." }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "f:=(x,y,z)->x^2+y^2+z^2;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 32 "g:=(x,y,z)->(x^2+y^2/4+z^2/9)-1;" }}}{EXCHG }
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "L:=(x,y,z,k)->f(x,y,z)+k*g(x
,y,z);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "L(x,y,z,k);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "eq1:=diff(L(x,y,z,k),x)=0;" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "eq2:=diff(L(x,y,z,k),y)=0
;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "eq3:=diff(L(x,y,z,k),z)=0;" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 26 "eq4:=diff(L(x,y,z,k),k)=0;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 35 "solve(\{eq1,eq2,eq3,eq4\},\{x,y,z,k\});" }}}
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