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Math Help - Proof: If a function f is convex on (a,b) then f is bounded below on (a,b)

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    Proof: If a function f is convex on (a,b) then f is bounded below on (a,b)

    Hi,

    i need to prove that , but i dont really know well convex function

    anyone can help me to solve that prove

    Prove that if a function f is convex on (a,b) then f is bounded below on (a,b)
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    Quote Originally Posted by neset44 View Post
    Prove that if a function f is convex on (a,b) then f is bounded below on (a,b)
    Choose two points c, d with a<c<d<b, and let L be the straight line through the points (c,f(c)) and (d,f(d)). The convexity of f ensures that the graph of f lies above the line L in the intervals (a,c) and (d,b). Also, convex functions are continuous, so f is bounded below by continuity in the closed interval [c,d]. Those facts together imply that f is bounded below throughout the interval (a,b).
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    thanx for help : )
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