let-f-x-and-g-x-be-twice-differentiable-functions-on-0-2-satisfying-f-x-g-x-f-1-4-g-1-6-f-2-3-and-g-2-9-Then-what-is-f-x-g-x-at-x-4-equal-to-

Question Number 10039 by Gaurav3651 last updated on 21/Jan/17

l e t f (x) a n d g (x) b e t w i c e d i f f e r e n t i a b l e

f u n c t i o n s o n [0, 2] s a t i s f y i n g

f^{″} (x) = g^{″} (x), f^{'} (1) = 4, g^{'} (1) = 6,

f (2) = 3 a n d g (2) = 9 . T h e n w h a t i s

f (x) - g (x) a t x = 4 e q u a l t o ?

Commented by prakash jain last updated on 22/Jan/17

f^{″} (x) = g^{″} (x)

\Rightarrow f^{'} (x) = g^{'} (x) + C

f^{'} (1) = 4, g^{'} (1) = 6

\Rightarrow 4 = 6 + C \Rightarrow C = - 2

f^{'} (x) = g^{'} (x) - 2

i n t e g r a t i n g

f (x) = g (x) - 2 x + C_{1}

f (2) = 3, g (2) = 9

3 = 9 - 2 \cdot 2 + C_{1} \Rightarrow C_{1} = - 2

f (x) = g (x) - 2 x - 2

f (x) - g (x) = - 2 x - 2

f (4) - g (4) = - 2 \cdot 4 - 2 = - 10

Commented by mrW1 last updated on 22/Jan/17

GREAT

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