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Differential Calculus

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2 Apr 2009 13:02:30 IST

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326

functions...a good ques,

None

f: R ---> R is a function such that

f(x)=x³+ x²f'(1)+xf'(2)+f'''(3)

for all x belongs to R..

then f(2)-f(1)= ........?

a)f(0)

b) -f(0)

c) f'(0)

d)-f'(0)

reply......

rates assured.....

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Comments (6)

radhika

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Joined: 30 Mar 2009

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2 Apr 2009 13:24:23 IST

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come on yaar!

T.S.K.SRAVANTH

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2 Apr 2009 13:38:06 IST

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f(x)=+(1)+x(2)+(3)

(x)=3+2x(1)+(2)

(x)=6x+2(1)

(x)=6

So,(3)=6 and (2)=12+2(1) ,(1)=3+2 (1)+(2)

Hence,(1)=-5,(2)=2

f(2)=8-20+4+6=-2 , f(1)=1-5+2+6=4 , f(0)=6

f(2)-f(1)=-6=-f(0)

vat kat

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2 Apr 2009 13:44:53 IST

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f'(x)=3x^2 +2xf'(1) +f'(2)putting 1 and 2 in x so we getf'(1)=-3f'(2)=-48so,f(2)-f(1)=-50which doesn't match wih any of the options but nearest ans comes out to be f'(0).

vat kat

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2 Apr 2009 13:45:50 IST

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saharsha kumar keshkar

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Joined: 7 Aug 2008

Posts: 1104

2 Apr 2009 16:00:55 IST

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f(x)=x³+x²f'(1)+xf''(2)+f'''(3)

f'(x)=3x² +2xf'(1)+f''(2)

put x=1...

f'(1)+f"(2)=-3..............................(1)

again.....

f"(x)=6x+2f'(1) , f'''(x)=6

put x=2...

f"(2)=12+2f'(1)................................(2)

on solving eqn(1) and (2)

we get....

f'(1)=-5 and f"(2)=2

f(x)=x³-5x²+2x+6

f(2)-f(1)=-6

which is ..... -f(0)

hence answer is (b)

nudge me if wrong.........

radhika

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Joined: 30 Mar 2009

Posts: 27

2 Apr 2009 16:56:00 IST

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thanx a lot!!!!!!!!!!

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