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Math Help - Simple Extreme Value Theorem Question

  1. #1
    Senior Member slevvio's Avatar
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    Simple Extreme Value Theorem Question

    I have asked too many hard questions recently now an easy one.

    Let  f: [a,b] \rightarrow \mathbb{R} be continuous. Then  \exists u,v \in [a,b] such that  f(u) \le f(x) \le f(v) for all  x \in [a,b].

    What if we have a function going to a subset of R, e.g. [-6, 7] or something, can we still use the EVT?
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  2. #2
    Junior Member
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    Yes, it still works. What we have is that [f(u),\,f(v)]\subseteq[-6,\,7]. The range of the function is [f(u),\,f(v)] so any codomain S\subseteq\mathbb R such that [f(u),\,f(v)]\subseteq S will be fine.
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