O
P->
E36Fihnd
d)
extremals
t
d
(iv)
(x+9)y'
o
Sal0)
Here
f-
Y
( y + y - 2 y sha) olt
the
O
inele pemelene
Ewlet 's ery
)ay
=
O
2y'
.c
's
Euler's eA
(3)
(+y)Y
unetion.als
he
y)y,whaek
t
ay
re comes
f
(Constudt)
Cenfplete selutin
e ey
CF
Y
13
PL.
Ge+C e+Sx
-
P-sl 4
Cutve
&4
the
unctional
y y y+ 4 y Cosx)olr
e
extremized
Set
Here
So
f
yy y
-2y +4 CrS
4y Cesd
y
valu
se
Nor
)
)
4 Cos- 2 y
2y
4 Csz-2y
+
A.E.
C.F=
Nor .1
4 (o)= 0, Y() =O
m
Y
2
=
Cos
o
C, Cos e r S She
D+I -cs)
m=t
Euleris
eg,.
for extan
dy
c
)4
hutegati
(iv)Hert
2y Shu
f
=2y-2Sim
O
3y
2y
Navr
Can
earuato
Eulets
e
UTide
as
)2y-2Simx
()o
-2
2 Y -2 Shn
y
Sim
Y
A.E.
m-1
D i ey
Co-efh c è
=o
m=
tha
CF
Now
RI. =
Cete
Sn.x)
S
ta
X
L Sm
2
Cens
here
F)-o
Ustraa
t
PI.
2
o
Cos ax
fet muula
Sha
2a
Da
Shm
Sinn (a
P.1
Na
fa)=
ad
ComLlete setutio
CCast C S
Condikibn
Usingtle
sm
0
=
0
x+
CCosO
+
C CasT+
Shux
(o)
Sim0
Ca Shm o+ 0
Cz
SimT
T+
+ TSheri
Sm
T ShT>
t t e writle
Nor
C
ShtT
anol
-
as
(T) = oP
C, =
o
r
fer
TShmls
(C+T) SimT
ASAiel
AS
Can
dnly
Are
Cutve
extremi'z ed
wrhich
the
ginvem