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1) If g(x) = -x^5 -x^4 +x^2 +1, prove that there is a number c such that g(c) = 1.
Can't u just put in a zero and get 1? I don't know how to prove it tho?
That's a perfectly good proof for that question, but other questions might not be as nice.
In general, you should find a value a such that g(a)<1, and another value b such that g(b)>1.
Then, because g(x) is a polynomial and therefore continuous, there will be a value c between a and b that gives g(c)=1.
Last edited by mathsyperson (2007-09-17 05:23:41)
Why did the vector cross the road?
It wanted to be normal.
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mathsyperson meant:
find a value a such that g(a)>1, and another value b such that g(b)<1.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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...Oops. Nice catch.
Why did the vector cross the road?
It wanted to be normal.
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