Page 158 - 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

5
4
3
B'N T[dkjoD 5H x d/ feBQK wkBK d/ bJh, cbB f (x) = x – 5x + 5x – 1, T[uso iK fBwBso
j?. f;ZX eo' fe x = 0 T[Zs/ fJj cbB Bk T[uso j? ns/ Bk fBwBso.
5
3
4
jZb L wzB fbU y = x – 5x + 5x – 1
d'jK gZyK dk x d/ ;kg/y fBy/VB eoB s/
dy
3
4
2
= 5x – 20x + 15x
dx
2
2
2
= 5x (x – 4x + 3) = 5x (x – 1) (x – 3)
dy
cbB T[usw iK fBT{Bsw wkB d/ bJh & 0
dx
2
∴ 5x (x – 1) (x – 3) = 0 ∴ x = 0, 1, 3
2
dy
3
2
2
j[D = 20x – 60x + 30x = 10x(2x – 6x + 3)
dx 2
x & 1 gqfs;Ekfgs eoB s/
2
dy
= 10 (2 – 6 + 3) = – 10 foDkswe
dx 2
∴ x & 1 T[s/ cbB T[uso j?.
x & 3 gqfs;Ekfgs eoB s/
2
dy
2
= 10× 3 (2× 3 – 6× 3 + 3) = 30(18 – 18 + 3)
dx 2
= 90 XBkswe
∴ x & 3 T[s/ cbB fBwBso j?.
x & 0 gqfs;Ekfgs eoB s/
2
dy
= 0, cbB T[uso j? iK fBwBso BjhA fejk ik ;edk.
dx 2
3
dy
2
j[D = 60x – 120 x + 30
dx 3
x & 0, gqfs;Ekfgs eoB s/
3
dy
= 0 – 0 + 30 = 30 i' Iho' BjhA j?.
dx 3
fJ; soQK x & 0 T[Zs/ cbB Bk T[uso j? ns/ Bk fBwBso.
T[dkjoD 6H cbB (x – 1) (x – 2) (x – 3) dk T[uso wkB gsk eo'.
jZb L wzB fbU y = (x – 1) (x – 2) (x – 3)
2
3
= x – 6x + 11x – 6
d'jK gZyK dk x d/ ;kg/y fBy/VB eoB s/
dy
2
= 3x – 12x + 11
dx
T[uso iK fBwBso wkB d/ bJh
dy
& 0
dx

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