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Math Help - Stationary points

  1. #1
    Member Furyan's Avatar
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    Stationary points

    Hello all

    I have a couple of questions.

    First, if the first derivative of a function is a quadratic can I show that the function has no stationary points by showing that the discriminant of the first derivative is less than zero?

    Second, how do I go about finding the range of the values of a for which
    y = x - (a/x) has no stationary points.

    I know the answer is that a is greater than or equal to zero, but I don't know how to get there.

    Thank you.
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  2. #2
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    Re: Stationary points

    Yep, that's correct, no stationary points within the reals.

    For the second question, what did you get as the derivative?
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  3. #3
    Member Furyan's Avatar
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    Re: Stationary points

    Thank you

    I got 1+ ax^-2
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  4. #4
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    Re: Stationary points

    That is correct, what conditions can we put on 'a' for it to have zeros?

    Think about a<0, a=0, a>0.
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  5. #5
    Member Furyan's Avatar
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    Re: Stationary points

    Hello

    I can see, I think, that if a = 0 then y=1 and that if a > 0, y > 1. When a < 0 I'm not sure.
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  6. #6
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    Re: Stationary points

    Quote Originally Posted by Furyan View Post
    When a < 0 I'm not sure.
    In this case there will be zeros. pick a few values i.e a=-1, -3, -100 etc. It will become clear.
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  7. #7
    Member Furyan's Avatar
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    Re: Stationary points

    Yes it has, crystal. I don't know why I didn't just do that in the first place. Thank you for your help.
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