f is continues on [a,b] A={x in [a,b]|f(x)=f(a)} prove that f(x) has a maximum f(supA)=f(a) ?? first of all there are two kinds of maximums here 1st a supremum which is inside [a,b] is called maximum and maximum of the function values correct??
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Originally Posted by transgalactic f is continues on [a,b] A={x in [a,b]|f(x)=f(a)} prove that f(x) has a maximum f(supA)=f(a) ?? first of all there are two kinds of maximums here 1st a supremum which is inside [a,b] is called maximum and maximum of the function values correct?? Extreme value theorem - Wikipedia, the free encyclopedia
Originally Posted by transgalactic f is continues on [a,b] A={x in [a,b]|f(x)=f(a)} prove that f(x) has a maximum f(supA)=f(a)? Because , you know that exists and . If it is true you are done. Else If you assume that leads to a contradiction to the continuity of . BTW: This not the Extreme value theorem.
Last edited by Plato; Aug 4th 2011 at 12:58 PM.
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