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Math Help - Using Taylor Polynoms for solving general problems

  1. #1
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    Using Taylor Polynoms for solving general problems

    Let f be derivative twice in (a,b) , and \forall x \in (a,b) : f''(x) \geq 0
    Prove / Give a negative example:
    \forall c,d \in (a,b) : f(\frac{c+d}{2}) \leq \frac{f(c)+f(d)}{2} .

    If that's a proof, then I'll have to use a Taylor Series to explain f(x), but how do I show that one side is smaller than the other?

    Thanks!
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  2. #2
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    Does anybody know how to solve this?
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  3. #3
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    suggestion

    Quote Originally Posted by adam63 View Post
    Let f be derivative twice in (a,b) , and \forall x \in (a,b) : f''(x) \geq 0
    Prove / Give a negative example:
    \forall c,d \in (a,b) : f(\frac{c+d}{2}) \leq \frac{f(c)+f(d)}{2} .

    If that's a proof, then I'll have to use a Taylor Series to explain f(x), but how do I show that one side is smaller than the other?

    Thanks!
    what would happen if we expand f(c) and f(d) also using taylor's series???then sum the terms.
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  4. #4
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    Quote Originally Posted by Pulock2009 View Post
    what would happen if we expand f(c) and f(d) also using taylor's series???then sum the terms.
    Hmm, but around which point? I tried to expand f(0.5(c+d)) one time around c, and one time around d, but it didn't really work...
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