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Math Help - Slopes of a Polynomial Function

  1. #1
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    Slopes of a Polynomial Function

    g'(x)=lim (g(x+h)-g(x))/h The limit is h>0
    This is the equation I got for slope.

    The actual problem is g(x)=2/(x-2) and I am asked to use the Difference Quotient and g(x) to find the slope.

    Please help and thank you
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  2. #2
    MHF Contributor
    Joined
    Mar 2007
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    Talking

    So follow the instructions:

    Evaluate g(x + h):

    . . . . . g(x\, +\, h)\, =\, \frac{2}{(x\, +\, h)\, -\, 2}

    Subtract g(x) from this:

    . . . . . \frac{2}{x\, +\,h\, -\, 2}\, -\, \frac{2}{x\, -\, 2}

    Convert to a common denominator:

    . . . . . \frac{2(x\, -\, 2)\, -\, 2(x\, +\, h\, -\, 2)}{(x\, -\, 2)(x\, +\, h\, -\, 2)}

    . . . . . \frac{2x\, -\, 4\, -\, 2x\, -\, 2h\, +\, 4}{(x\, -\, 2)(x\, +\, h\, -\, 2)}

    . . . . . \frac{-2h}{(x\, -\, 2)(x\, +\, h\, -\, 2)}

    Then you divide by h. Where are you stuck?

    Please be complete. Thank you!
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