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February 21st, 2012, 08:29 PM   #1
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3 doubts- plz help!!

Kindly help me with the following 3 questions and please tell me how you arrived at the answer. Thanks in advance

Let f and g be two differentiable functions on (0, 1) such that f(0) = 2, f(1) = 6, g(0) = 0 and g(1) = 2. Then there exists ? ? (0, 1) such that f'(?) equals
(a) (1/2)g'(?),
(b) 2g'(?),
(c) 6g'(?),
(d) (1/6)g'(?).

If f(1) = 0, f'(x) > f(x) for all x > 1, then f(x) is
(a) positive valued for all x > 1,
(b) negative valued for all x > 1,
(c) positive valued on (1, 2) but negative valued on [2,?).
(d) None of these.


For all x, y ? (0, ?), a function f: (0, ?) --> R satisfies the inequality
|f(x) - f(y)| ? cube(|x - y|). Then f is
(a) an increasing function
(b) a decreasing function
(c) a constant function
(d) None of these.
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February 22nd, 2012, 03:38 AM   #2
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Re: 3 doubts- plz help!!

Someone please answer!!
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February 22nd, 2012, 05:18 AM   #3
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Re: 3 doubts- plz help!!

Quote:
Originally Posted by vasudha
Let f and g be two differentiable functions on (0, 1) such that f(0) = 2, f(1) = 6, g(0) = 0 and g(1) = 2. Then there exists ? ? (0, 1) such that f'(?) equals
(a) (1/2)g'(?),
(b) 2g'(?),
(c) 6g'(?),
(d) (1/6)g'(?).
Cauchy's mean value theorem:



Quote:
If f(1) = 0, f'(x) > f(x) for all x > 1, then f(x) is
(a) positive valued for all x > 1,
(b) negative valued for all x > 1,
(c) positive valued on (1, 2) but negative valued on [2,?).
(d) None of these.
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February 22nd, 2012, 07:13 AM   #4
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Re: 3 doubts- plz help!!

Thank you greg
But I haven't got the 2nd question. We are just given that f'(x)>f(x) for all x>1.. how did you say that f'(1)>f(1)?? Please reply.
And I would be very grateful to anyone who can help me with the 3rd question as well..
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February 22nd, 2012, 07:30 AM   #5
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Re: 3 doubts- plz help!!

I made an error on that one, my apologies.
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