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Math Help - critical points - maximum, minimum, or point of inflection?

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    critical points - maximum, minimum, or point of inflection?

    Ok so I get how to find the critical points but I don't understand how you tell if it's mmaximum, minimum, or point of inflection. Say I have one point (-2,-16), what would it be?
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    Re: critical points - maximum, minimum, or point of inflection?

    Quote Originally Posted by needprecalchelp View Post
    Ok so I get how to find the critical points but I don't understand how you tell if it's mmaximum, minimum, or point of inflection. Say I have one point (-2,-16), what would it be?
    You'll have to excuse me, but my mind-reading ability is slipping terribly. Would it be too much to ask you to provide a bit more information about the function that generates the value f(-2) = -16 ?

    One more small item ... you understand that determining what you want answered will most probably require analysis using the second derivative, a calculus topic?
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    Re: critical points - maximum, minimum, or point of inflection?

    no this is from precalc class. The original question is f(x) = x^2 + 4x -12 and I'm supposed to find the critical points for the function and determine whether each point is a maximum, minimum, or point of inflection. I found the critical point to be (-2,-16).
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    Re: critical points - maximum, minimum, or point of inflection?

    Quote Originally Posted by needprecalchelp View Post
    no this is from precalc class. The original question is f(x) = x^2 + 4x -12 and I'm supposed to find the critical points for the function and determine whether each point is a maximum, minimum, or point of inflection. I found the critical point to be (-2,-16).
    note that the graph of f(x) is a parabola that opens upward ... what does that tell you?
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    Re: critical points - maximum, minimum, or point of inflection?

    That it's minimum. But how can I find out without graphing?
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    Re: critical points - maximum, minimum, or point of inflection?

    Quote Originally Posted by needprecalchelp View Post
    That it's minimum. But how can I find out without graphing?
    I don't understand ... knowing that the graph of f(x) is a parabola is basic knowledge.

    If you can't use that information, then you would need to use calculus.
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