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Math Help - Relative Minimum

  1. #1
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    Question Relative Minimum

    What is the relative minimum for y = x + 1/x
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by nath_quam
    What is the relative minimum for y = x + 1/x
    A local minimum of a function can be found by differentiating the function
    and solving for the zeros of the derivative. These zeros comprise local
    maxima, minima and points of inflection, so you will need to confirm
    which of these any such zeros is.

    <br />
y=x+1/x<br />
,

    so:

    <br />
\frac{dy}{dx}=1+(-1)/x^2<br />

    So we are looking for solutions of:

    <br />
1-\frac{1}{x^2}=0<br />

    which with a bit of algebraic jiggery-pokery we find are:

    x=\pm 1,

    and a bit more work shows that x=1 is a local minimum,
    and x=-1 is a local maximum.


    RonL
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  3. #3
    TD!
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    Solve dy/dx = 0, you'll find a relative min and max.
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