Page 156 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math9-1 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 cbB d/ T[usw iK fBT{Bsw wkB d/ bJh

dy
= 0
dx
2
3
∴ 4x – 24x + 44x – 24 = 0
3
2
iK 4(x – 6x + 11x – 6) = 0
2
3
iK x – 6x + 11x – 6 = 0
iK (x – 1) (x – 2) (x – 3) = 0
∴ x = 1, 2, 3
;whH (i) d/ d'jK gZyK dk x d/ ;kg/y fBy/VB eoB s/
d 2 y
2
= 12x – 48x + 44
dx 2
d 2 y
2
x = 1 T[Zs/ dk wkB = 12(1) – 48(1) + 44
dx 2
= 12 – 48 + 44
= 8 = XBkswe okPh
fJ; soQK x = 1 T[Zs/ cbB dk wkB fBT{Bsw j?

d 2 y
2
x = 2 T[Zs/ dk wkB = 12 (2) – 48(2) + 44
dx 2
= 48 – 96 + 44

= – 4 = foDkswe okPh
fJ; soQK x = 2 T[Zs/ cbB dk wkB T[usw j?

d 2 y
2
x = 3 T[Zs/ dk wkB = 12 (3) – 48(3) + 44
dx 2
= 108 – 144 + 44
= 8 = XBkswe okPh

fJ; soQK x = 3 T[Zs/ cbB dk wkB fBT{Bsw j?.
3
2
T[dkjoD 3H x – 2x + x + 6 dk T[uso ns/ fBwBso wkB gsk eo'.
3
2
jZb L wzfBnk y = x – 2x + x + 6
dy
2
= 3x – 4x + 1
dx
d 2 y
ns/ = 6x – 4
dx 2
dy
j[D = 0 oZyD s/
dx
1
2
3x – 4x + 1 = 0 iK (3x – 1) (x – 1) = 0, fi; Bkb x = iK 1
3

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