Math 474 :
Dy 7
.
Shifty
Df
.
.
gas to plane
the tayut hdiatix
ones
f
.
.
.
mit speed pre method diltklk
as )
an
-
a
← @
.
amatemtthjqt
Fun tgh as )
And the
mit speed
is
f
length
Tls )
,
Cms
Tls ) lies
,
the
B
Has
=
mit
the
an
prokbf
B
tarot indium
the
told curvature
For plane
Tls )
are
) ds
ask
,
net
Tuft
.
told
fan tune wah
,
cwntu
Doh Hlds
f
'
=
it
so
an
be
=
a
4)
.
Tls )
TI 21
aegis
is the
hooked
3,
"
s 's )
.
:
x
length
=
problem
'
IT HI
T 10 )
by
( Tls ) )
ate
san
Ots )
:
toe
.
While
0
af
is
well
li ) O' Is)
Iii ) Als)
Df
The
:
rokk
wheel
the
sp Tf
:
als
)
Pf Tls ) not
:
B
S
=
a
!
0
'
the
a
,
so
fat
citing
wean
,
que
tut Oto)
is
btw
0
hit
&
,
olefins
is
061
gin
by
it Wkt an
index
naef
old )
-
f
as )
one
a
dosed plane
be dead
multiple
defined
-
plane
kph
a
lddu +0+0 )
zttlotll
=
is
well
is
f
index
I
defined up to
-
ad
.
are
&
'
,
all st ditn
I
by
B
a
an
iwtgr
multi
f
.
2 it
.
a
so
then
.
.
.
#
:
§%
*[
*
Exapbt
:@
NO
,
)
"
"
I
.
'
'
't
-
g€my
*
"
o
,
*
1
"
I
=
+1
.
4
'
+2
"
%€3Eg/
g@?g%H
6
7
z
4
o
'
I
=
+1
2
a
a
Thy : A Siple
dyed
The idea
it
Df
:
A
,
tht
]
plane
costs
plane came
as
is
(
lie
we
mh
ate
4
,
to
if it
convex
no
self
mthat
from
escape
lies
-
on
) by nkth
jzoohet
a
II
index
.
"
f erh
site
me
'S
as
you gained by going
of ib
trot
*on
g
in
.
lines
.
-
Nm
Convex
Eguislntf
,
a
are
B
crux
if
.
Convex
ay
two
pnb
Nan
an
-
-
convex
the
convex
cure
an
he
connected
by
a
the
squt
lying
inside the
one
Df A wkx
f
:
)
one
plane
.
is
a
pont
nsIs
pm
true
The bsr
1 though
idea
WAY
the
&
by
it )
atndrhh
by
[
on
°
At
convexity
wtex
a
Sign
'
K Is )
,
troy bit
By switchg signs
+ By 4)
tie
f
.
,
A ,B
,
+0k G)
'
if
C
>
so
.
so
( ht
asir
als )
sppse
hs
a
ht
,
opposite
on
arum
f
critical point
wtus
.
also myhe
me
is
sprig )
paemettdhg
last 2 votes
at
be the
&J
p
Em
.
arc
at
to
lgth
dls )
f
a
both p &
8
m
necessary
J
Slot Axlslt By 4)
Harm
,
I
claim th
.
}
D
the
cause
RIS )
is
is
,
l
]
Since
.
§Llsd
I
=
continuous
,
.
.
we
atndrth
tht the
ae
no
other
WAS
hue
,
+
C)
'
K 's ) ds >
impossible
.
an
a
moth
; then K Isl
'
one
Axt By
be the
too
,
f
.
.
0
Hence
.
o
&
=
,
us
[
on
guk
fl
Axt By
P
.
g./
•
on
amzyf ,
were
his
as
sales of L
for the she
assume
ht Axt By
:
which D
&
the opposite sin
&
a
xlsikf
Now
=o
p
on
Now tunes He
1 Adsl
p
,
,
f#
-
48
e) ,
,
9
Now by
,
I
o
.
straight line L
a
cwehs at last 4
ones
any
min
a
plane
pm
HD
pre
max
a
f
are
wait
he
to
B
it his
Car nut
this mtk
=
Gi
0
Q
Fowlkrtxtht A siple dead
will
)
'
x
:
We
when
0
.
It
>
o
Axt Bytc
j
< o
too
fall
First
sine
,
}
,
×
parametrized
261=1×141
R↳)=1x" 41
and hence
'
K 's )
so
Lenny
For
.
Oil b)
=
real
my
llx
=
' '
's )
Hence
.
'
's ) )
B C
,
Paf
kitty 'W= (
Since
x
"
4)
=
=
bth
Since
x
"
'D &
§x" Yds
Bit then
y
-
'
"
y
4)
ad
't
0
=
,
O' G)
y
,
"
'
0=4 "Hds=f !
cos
,
we
slds
y 's )
-
is
we
of !
y
'
's )
0
To
ds
'
Since
folaxlsltylsl
In
fly 610
"Hds=S
the
puff
=
!
O' Is)
+40
'
'
.
so
man
write
=
FED
'
=
O' 61
,
fan :
=o
have
y "ls)=
cos lots ) )
&
y
'
's )
public
are
O' Is )
Its ) O' G)
.
,
.
O' Is )ds
-
'
'
x
-
lslds
's )
{
Now mtgnte by prlz
.
:
OH
u=
du
'
O' lslds
=
Ylslds
4151
u=
'
ylsl O' lslds
ds=o
the
.
'H0' lslds
O' 10 )
=0
=
same
flxlsl
-
he
new
game goes
'
A lslds
.
hue
,
=
AS !xH0" Holst
the Four Votexthm
third whx
,
yka.gl#oEfoyHo'Has
=
So
vector
)|= fnftplolssfcosyotsyoypp
du=
=
them tht
unit
.
(
're
a
,
&
'
x 's )
4) )
lots) ) as )
come
=
'
x
lots ) ) , s.ir/ots)D
lslds
''
wash s.nl#sD)
's )
,
'
y
,
lots ) ) O' G)
sir
-
kits )
=
cntndrth will
S!( Axlsltbyls ) +40
:
,
HHIO ' 's )
sir
-
,
,
( cos
=
desired
or
A
numbers
y
small
"
y
,
,
arckyth
by
jls )
,
win
'
BTOYHO 'D dst Cfo 0 's
mshmthtk
"
'k) myt
'
dye
syn
)ds=0
on
•
.
either
par 8
lor both mkga
,
Anti
sin
f
'=
Ig|
K
Since
53
at
her
both
s
,
&
min
ats
,
,
sign
f
1214 ) is
negate
mstbeafthwkx
the
in
oil
,
mx
here
=g⇐g
Sine
mx
at
her
both
s
,
&
min
ats
,
,
sign
f Hls )
,
positive