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Topic: Mean Value Theorem (Read 615 times) |
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KeyBlader01
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Mean Value Theorem
« on: Oct 24th, 2008, 7:50pm » |
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Assume that f is a differentiable function such that f(0)=f '(0)=0. Show by example that it is not necessarily true that f(x)=0 for all x. Find the flaw in the following bogus "proof". Using the Mean Value Theorem with a=x and b=0, we have f '(c)= f(x)-f(0) / x-0. Since f(0)=0 and f '(c)=0, we have 0=f(x)/ x so that f(x)=0.
For the first part, we did that in class. We were able to prove that if we picked a function such that f(x)= x^2 and f '(x)=2x. Then it would disprove the first part because we're showing that f(x) =/= 0 for all x. The second part, our professor said there is something wrong with it. What is the wrong information the previous part was using in the proof in the second part? I'm confused at what the problem is asking. Can someone explain the problem from the beginning and go in steps?
Thanks a lot!
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towr
wu::riddles Moderator
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Some people are average, some are just mean.
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Re: Mean Value Theorem
« Reply #1 on: Oct 25th, 2008, 5:22am » |
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Where does f '(c)=0 come from?
It's plainly not true for f(x)=x2 and c in the open interval (0,x)
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Wikipedia, Google, Mathworld, Integer sequence DB
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