{VERSION 3 0 "IBM INTEL NT" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Comment" 2 18 "" 0 1 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 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "page 197 number 28:" }}
{PARA 0 "" 0 "" {TEXT -1 64 "Find the shortest distance from the curve
  xy =4  to the origin." }}{PARA 0 "" 0 "" {TEXT -1 120 "First we plot
  y = 4/x, and let the distance function, d(x), to be the distance fro
m the curve to the origin. Thus d(x)=" }{XPPEDIT 18 0 "sqrt(x^2+(4/x)^
2);" "6#-%%sqrtG6#,&*$)%\"xG\"\"#\"\"\"F+*$)*&\"\"%\"\"\"%\"xG!\"\"\"
\"#F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "To minimize the functi
on d(x) is equivalent to minimize d^2, let's call it e(x)." }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "e:=
x->x^2+(4/x)^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "f:=proc(
x) diff(e(x),x) end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "simplify(f(x));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "factor(f(x));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(f(x),x=-3..3,y=-30..30);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 247 "As we see from the graph of  f (d
erivative function of  e(x)), we have a relative minimum for e(x) at  \+
x = -2  and x =2. This means that the point (2, 2) is the point on  xy
 = 4 which will result in the shortest distance. The shortest distance
 is " }{XPPEDIT 18 0 "sqrt(2^2+(4/2)^2);" "6#-%%sqrtG6#,&*$\"\"#\"\"#
\"\"\"*$*&\"\"%F*\"\"#!\"\"\"\"#F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "plot(4/x,x=-5..5,y=-10..10);" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 12 "Problem #27:" }}{PARA 0 "" 0 "" {TEXT -1 92 "Suppose t
hat a rectangle has its base on the x-axis and its two upper corners o
n the curve  " }{XPPEDIT 18 0 "y = 2(1-x^2);" "6#/%\"yG-\"\"#6#,&\"\"
\"\"\"\"*$)%\"xG\"\"#F*!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "(
a) What is the maximum perimeter of such a rectangle." }}{PARA 0 "" 0 
"" {TEXT -1 54 "(b) Show that there is no minimum perimeter rectangle.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "plot(2*(1-x^2),x=-5..5,y=-5..5);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "14" 0 }{VIEWOPTS 1 1 0 1 1 1803 
}