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Math Help - Help in mean value theory

  1. #1
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    Help in mean value theory

    I don't know how to use mean value theorem to show that
    e^x >= 1+x+ 1/2 x^2 for x>0
    I hope someone can give me some advises.
    Really thanks.
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  2. #2
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    You don't really need the mean value theorem here (though you do need basic knowledge of Taylor Series), because it can be shown that

    \displaystyle e^x = \sum_{n = 0}^{\infty}\frac{1}{n!}x^n

    \displaystyle = 1 + x + \frac{1}{2}x^2 + \frac{1}{3!}x^3 + \frac{1}{4!}x^4 + \dots

    \displaystyle \geq 1 + x + \frac{1}{2}x^2.
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  3. #3
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    I know it can use Taylor theorem .
    But I want to use another way to do it.
    So I am thinking whether mean value theorem can do it or not.
    And want to try it
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