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November 18th, 2010, 02:17 AM   #1
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Nice-Please help

1. Let be a continuous function on and differentiable on for all . Prove that there exists so that

2. Find the least value of
where a,b,c are real numbers satisfying and
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November 18th, 2010, 02:43 AM   #2
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Re: Nice-Please help

I'm really curious what does "<>" mean.
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November 18th, 2010, 04:14 AM   #3
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Re: Nice-Please help

Quote:
Originally Posted by stainburg
I'm really curious what does "<>" mean.
Sorry
<> is not =.
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November 18th, 2010, 05:07 AM   #4
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Re: Nice-Please help

As far as I know, I don't think there is such a function satisfied such conditions.
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November 18th, 2010, 08:23 AM   #5
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Why? The function f(x) = 1 satisfies them.
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November 18th, 2010, 09:06 AM   #6
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Re:

Quote:
Originally Posted by skipjack
Why? The function f(x) = 1 satisfies them.
, which means codomain of f(x) is the whole , not just a single point
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November 27th, 2010, 06:43 PM   #7
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That's a logical interpretation, but I'm not sure whether it's the intended interpretation. Perhaps TungLHang can clarify what was meant.
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November 27th, 2010, 07:15 PM   #8
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Re:

Quote:
Originally Posted by skipjack
That's a logical interpretation, but I'm not sure whether it's the intended interpretation. Perhaps TungLHang can clarify what was meant.
Yeah, maybe. I compose a function g(x)=ln[f(x)], for which g'(x)=f'(x)/f(x), apply the Lagrange's mean value theorem on g(x), still find nothing. And what is the relationship between f(a) and f(b)? If not, it doesn't make any sense
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