Page 30 - Math Grade 12 (Advance)

PROEUS DARA

1:?1018 f'(x) = 2x 3

3
f'(x) = 0 r;sm 2x 3 = 0 , X = -
2
" 3
b'l:Hli ZE(l, 2) '1

Lff'H11g : R. tti2J f(x) = i -- 2x '1 ~RL?ltl c E [0, 2] Gtlbli f'(c) = 0 '1

~ 2 I C)
2. l:ti<:~J f(x) = (x 3)(x+ 1) 1RLti'U cE [-1, 3] f:tlbli f'(c) = 0 '1

4.

d5 f dl~8ti'iH~·dltinlirstsH [a, b] 1:f181:tlhHru (a, b) &S"H1:f18 cE (a, b)
I GV
'i:H15tmb~rs &'tlru f'(c) = f(b)- f(a) '1
u b-a

I I C) I c:t,t 0 ~ Q)
Mfffll1J11rrl1 1'i : 21 S1 r; tl ru fflfi nl'i:Hl ~u rul ts (a, f(a)) 8b (b, f(b)) 1:f18 fU'f§ ill~
l..i C9- "' 1
y = [f(b)-f(a)\x-a)+f(a)
b-a J

mb g(x) = f(x)- y
y
m012 :

g(x) = f(x)-[f(b)---f(a)J(x-a)-f(a)
b a
g'(x) = f(x)-f(b)-f(a)
b-a
0
mmg x = a 1:?1018 g(a) = 0
b X
X C
8r;mg x = b 1:?1012 g(b) = o

t1'::lH15 g(a) = g(b) = o nl'f§~ghfug~ru 1:f18G88 cE (a, b) 'i:H15tmb~tsttjru
t_; " u u u
g'(c) = 0 l:tfl ru g'(c) = f'(c) -- [f(b)- f(a)J = 0 sl 2~018 f'(c) = f(b)- f(a)
b-a il b-a
tltit881:f18G88 cE (a, b) 'f§l11Mb~rsttlru f'(c) = f(b) f(a) '1
u w w b-a
wtmtftrt: 151rJQJttlt5~~thsbLffl'lHilb f(x) = i Lnci a;b Lf15t5Sbt5~~&[:jru

2 2
Fil~fil'h\jbliEJci A(a, a ) Sb B(b, b ) '1
Gtfw : t dlH~?J'f§smtisbffi~Hd'h~r;ru (a, b) m'f§t¥~159S'l~~'f§uj'f§1:fls

cE (a, h) 'f§Li1Mb~GGtlbli f(b)-f(a) = f'(c) (I)
w b-a

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