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Math Help - Showing theres no maximum to a function

  1. #1
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    Showing theres no maximum to a function

    I have the following function:

    f(x)=6x^2-x-2

    I've worked out the derivative of this function:

    f'(x)=12x-1

    I've also worked out the minimum:

    (\frac{1}{12}, \frac{-49}{24})

    However, I am unsure how I can prove/show that there is no maximum to this function?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Showing theres no maximum to a function

    Quote Originally Posted by richtea9 View Post
    However, I am unsure how I can prove/show that there is no maximum to this function?
    If there is a relative maximum at x_0 , necessarily f'(x_0)=0 so the function has no relative maximum. If you ask for absolute maximum take into account that \lim_{x\to +\infty}f(x)=\lim_{x\to -\infty}f(x)=+\infty , so f has not absolute maximum either.
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