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Math Help - <please help me>

  1. #1
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    <please help me>

    suppose \ that  \ f:[a.b] \to R \ is \ continuous \ with \ f(x)>0 \ , \forall x \in \ [a,b] <br /> <br />
. prove \ that \ \exists c>0 \ such \ that \ f(x) >c , \forall x \in [a,b]
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  2. #2
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    Quote Originally Posted by flower3 View Post
    suppose \ that  \ f:[a.b] \to R \ is \ continuous \ with \ f(x)>0 \ , \forall x \in \ [a,b] <br /> <br />
. prove \ that \ \exists c>0 \ such \ that \ f(x) >c , \forall x \in [a,b]
    Do you know that a continuous attains its minimum and its maximum of a closed interval?
    If so then \left( {\exists d \in [a,b]} \right)\left( {\forall x \in [a,b]} \right)\left[ {f(x) \geqslant f(d) >\frac{{f(d)}}{2} > 0} \right]
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