Re: prop 21,Q8

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Posted by Terence Tao on March 07, 2003 at 10:54:26:

In Reply to: Re: prop 21,Q8 posted by stefan on March 07, 2003 at 00:42:34:

>actually, now I realize you need a=b to use rolle's theorem and the max/min principle to show that if f'(x)=0 for all x, then f(x) is the constant function, but I still think it messes up part (a) and part (b).

>>I think the condition a<=b should be aYou're right; Proposition 21 should be rewritten with the hypothesis
that a < b. As stated the proposition is false because one cannot
differentiate a function defined on just a point.

Terry

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>>actually, now I realize you need a=b to use rolle's theorem and the max/min principle to show that if f'(x)=0 for all x, then f(x) is the constant function, but I still think it messes up part (a) and part (b). >>>I think the condition a<=b should be a<b in order for the result to be true. In other words to get strictly greater than or less zero we can't have a=b. >You're right; Proposition 21 should be rewritten with the hypothesis >that a < b. As stated the proposition is false because one cannot >differentiate a function defined on just a point. >Terry
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