Page 166 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math10-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

noEPk;soh dk rfDs

B'N ∂ 2 u ∂ 2 u ∂ 2 u
= 6x + 2,⋅ = 2, =− 1 HHH(3)
x ∂ 2 x ∂ 2 ∂∂
xy
(0, 0) wkBK d/ bJhl
∂ 2 u ∂ 2 u
+
= 6(0) 2 = > 0, = 2 >
0
2
x ∂ 2 y ∂ 2
∂ 2 u ∂ 2 u  ∂ 2 u  2
⋅
( 1) =
= 2 2 = >   =− 2 1
4
x ∂ 2 y ∂ 2  ∂∂ 
x y
fJ; soQK, (0, 0) w[Zb, fBwBso PosK B{z ;zs[PN eodk j?.
2
2
3
u = x + x – xy + y + 4 = 4 (0, 0) w[Zb fpzd{ T[Zs/ fBwBso w[Zb j't/rk.
fpzd{ (–1/2, –1/4) d/ bJh,
∂ 2 u  1  ∂ 2 u
= 6 −  + 2 =− 1, = 2

x ∂ 2  2  y ∂ 2
∂ 2 u ∂ 2 u  ∂ 2 u  2
( 1)2 ( 1) =− <
−   = − − − 3 0
x ∂ 2 y ∂ 2  ∂∂ 
x y
fpzd{ (–1/2, –1/4), gbkfJD fpzd{ fdzdk j?.
BshfinK B{z ;zy/g o{g ftZu j/m nB[;ko fbfynk ik ;edk j?.

2H fBZu/ fdZs/ j'J/ cbB dh ;jkfJsk Bkb u dk uow w[Zb gsk eo'l
3
3
y = x + y – 3x – 27y + 24
jZb L gfjbh Pq/Dh dhnK PosK
2
2
f x = 3x – 3 = 0, x – 1 = 0
2
2
f y = 3y – 27 = 0, y – 9 = 0
∴ (1, 3), (1, ^3), (^1, 3), (^1, ^3)
d{ih Pq/Dh dhnK PosK
f xx = 9x
f yy = 9y
f xy = 0
(1, 3) d/ ;zdoG ftZu
f xx = 9x = 9 > 0
f yy = 9y = 27 > 0
2
f xx f yy – (f xy ) = 243 – 0 = 243 > 0

160 LOVELY PROFESSIONAL UNIVERSITY