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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

wkB fBwBso (minimum) j?, fJ;dk noE e/tb fJj j? fe fJ; fpzd{ d/ nk;gk; tkb/ d'B'A B'N
fpzd{nK T[Zs/ e'fN dk wkB ;G s'A xZN j?.

9H3 T[uso ns/ fBwBso gsk eoB d/ gqshpzX
(Condition to Finding Maxima and Minima)

fe;h fpzd{ x = a T[Zs/ cbB y = f (x) d/ T[uso iK fBwBso wkB gsk eoB d/ gqshpzX fBwB jB^
(i) Io{oh gqshpzX (Necessary Condition)
T[uso (maximum) ns/ fBwBso (minimum) d'jK d/ jh bJh Io{oh gqshpzX fBwB jB^
dy
f ’ (x) = 0 iK = 0
dx
(ii) T[fus gqshpzX (Sufficient Condition)

T[uso (maximum) ns/ fBwBso (minimum) d/ bJh T[fus gqshpzX j/m nB[;ko jB^

T[uso (maximum) d/ bJhL

2
dy
x = a T[Zs/ 2 dk wkB & foDkswe
dx
okPh fBwB (minimum) d/ bJh L
dy
2
x = a T[Zs/ dx 2 dk wkB & XBkswe

;t?^w[bKeD (Self Assessment)

1H ykbh ;EkBK dh g{osh eo' (Fill in the blanks)^
1H rfDs dk fJZe w[Zy T[g:'r fe;h HHHHHHHHHHHHH d/ T[uso ns/ fBwBso wkB gsk eoB ftZu
j[zdk j?.
2H fe;h cbB d/ pj[s ;ko/ T[uso ns/ HHHHHHHHHHHHHHHH wkB j' ;ed/ jB.
2
dy
3H HHHHHHHHHHH d/ bJh x = a T[Zs/ dk wkB foDkswe j[zdk j?.
dx 2
2
dy
4H fBwBso d/ bJh x = a T[Zs/ dk wkB HHHHHHHHHHH j[zdk j?.
dx 2

9H4 T[uso iK fBwBso fe;h d/ th Bk j'D dk gqshpzX
(Conditions to Absent of Maxima or Minima)
fpzd{ x = a T[Zs/ cbB y = f (x) Bk sK T[uso j't/rk ns/ Bk jh fBwBso j't/rk, i/eo
dy dy
3
2
dx 2 dk wkB & 0 ns/ dx 3 dk wkB ≠ 0

T[uso ns/ fBwBso wkBK d/ r[D L
1H T[uso wkB d/ pknd fBwBso wkB ns/ fBwBso wkB d/ pknd T[uso wkB nkT[Adk j?
Gkt T[uso ns/ fBwBso wkB J/eKso eqw Bkb nkT[Ad/ jB.

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