Page 148 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math8-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

vFkZ'kkfL=k;ksa dk xf.kr

uksV ;gk¡ ldy ykHk π ( oqQy vkxe ' ( oqQy ykxr +

oqQy vkxe ' ( ewY; ; oLrq dh ek=kk
( ( !+ * ( !+ *

∂ R ∂
' ( = (30x − x 2 ) = 30 − 2x
x ∂ x ∂

blh izdkj + ( , , 0
∂ C
+ ( = 2x + 6
∂ x
larqyu dh n'kk esa ' ( +
!+ * ( ,

;k *$ ( *!+ , ( * $
24
;k ( = 6
4
dk eku nwljh rjg Hkh fudkyk tk ldrk gSµ

π ( ' * ( !+ * * , , 0

(!+ * * * * 0
( $ * * 0

osQ lanHkZ esa vodyu djus ij
∂π ( $ * $
x ∂
∂π
vf/dre ykHk osQ fy, ( + ;k $ * $ ( + ;k * $ ( $ ;k (
x ∂
2
∂π
vf/dre ykHk dh f}rh; 'krZ < 0
∂ x 2
2
∂π
vr% = 4 < 0 vr% ;g 'krZ iw.kZ gksrh gSA
x ∂ 2
ek¡x iQyu esa ( $ j[kus ij
( !+ * ( !+ * $ (

ldy vkxe ' ( !+ *
( j[kus ij
' ( !+ ; * ; ( 8+ * ! ( $$

blh izdkj π ( $ * * 0 ( ( j[kus ij)
( $ ; * ; ; * 0
( $$ * 0 * 0 ( &

mnkgj.k 8- ;fn iw.kZ izfr;ksfxrk osQ vUrxZr fdlh iQeZ dk oqQy ykxr iQyu]

! #
%&
gks rks bldk iwfrZ iQyu Kkr djksA