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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

noEPk;soh dk rfDs

B'N ∂π
tZX s'A bkG d/ bJh & 0 iK 24 – 4x = 0 iK –4x = 24 iK x = 6
x ∂
∂ π
2
tZX s'A tZX bkG dh d{ih Pos < 0
x ∂ 2
∂ π
2
fJ; soQK 4 =< fJ; soQK fJj Pos g{oh j[zdh j?.
0
x ∂ 2
wzr cbB ftZu x = 4 oZyD s/

;eb nkrw

fJ;h soQK

T[dkjoD 8H i/eo g{oD gqsh:'frsk d/ nzsors fe;h cow dk e[ZbQ bkrs cbB,
3
2
C = 0.3x – 3x + 20x + 15
j't/ sK fJ;dk g{osh cbB gsk eo'.
jZb L n;hA ikDd/ jK fe g{osh cbB d/ bJh
P ≥ AVC fJZE/, P = w[Zb, AVC & n";s gfotosBPhb bkrs

TVC TC -TFC
;kB{z gsk j? fe AVC = =
x x
fJZE/ TVC = e[ZbQ gfotosBPhb bkrs, TC = e[ZbQ bkrs, TFC e[ZbQ ;fEo bkrs ns/ x = t;s{
dh wksok j?. fJ; bJh

(∵ TFC = 15)

∂ ( AVC ) ∂ 2 ( AVC )
AVC B{z fBT{BswheoD eoB s/ = 0 ns/ > 0
x ∂ x ∂ 2

2
∂ ( AVC ) ∂ (0.3x + 3x + 20 )
fJ; soQK = = 0.6x −=
3 0
x ∂ x ∂
iK 0.6x = 3 fJ; soQK x = 5
∂ 2 ( AVC )
0
= 0.6 > fJ; soQK x = 5 T[Zs/ AVC fBT{Bsw j't/rh.
x ∂ 2
fBT{Bsw AVC eZYD d/ bJh x = 5 oZyD s/
AVC = (3 × 5 × 5) – (3 × 5) + 20
= 7.5 – 15 + 20 = 12.5
i/eo P < AVC = 12.5, T[sgkdB ;so Iho' j't/rk.
i/eo P > AVC = 12.5, T[d'A g{osh ;so XBkswe j't/rk.

132 LOVELY PROFESSIONAL UNIVERSITY