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VED1
E L-LOVELY-H math9-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

fJekJh^9 L T[uso ns/ fBwBso L fJZe uo

2
T[dkjoD 9H i/eo y = a log x + bx + x d/ x = – 1 ns/ x = 2 T[Zs/ T[uso^fBwBso wkB B'N
(extremum values) jB sK a ns/ b d/ wkB gsk eo'.

2
jZb L y = f (x) = a log x + bx + x ⇒ dy = 1 2 a. + 1bx +
dx x
dy
T[uso^fBwBso d/ bJh, = 0,
dx

⇒ ....(i)

ns/ ....(ii)

(i) ns/ (ii) B{z jZb eoB s/
1
a = – 2, b = – T[Zso
2

T[dkjoD 10H cbB x + sin 2x, (0 < x < 2π) d/ T[uso iK fBwBso wkB gsk eo'.
jZb L wzB fbU y = x + sin 2x
dy
1 2cos2x
∴ =+
dx
dy = 0 gqfs;Ekfgs eoB s/, 1 + 2cos 2x = 0
dx

iK

π 2π
fJ; soQK [∵ 0 < x < 2π] ⇒ x = ,
33
j[D

π
(1) id'A x =
3
2
dy =− 4sin 2 =− 4   3π  =− 2 3 foDkswe
dx 2 3   2   
π
∴ x = T[Zs/ cbB T[uso j?.
3
π
ns/ fdZs/ j'J/ cbB ftZu x = gqfs;Ekfgs eoB s/, cbB dk T[uso wkB
3
π 2π π 3 2π+ 33
= + sin = + = T[Zso
3 3 3 2 6
2π dy 4π
2
(2) id'A x = sK =− 4sin
3 dx 2 3

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