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Math Help - Show that there are no tangents to the curve y = (x+2)/(3x+4) with a positive slope.

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    Show that there are no tangents to the curve y = (x+2)/(3x+4) with a positive slope.

    Show that there are no tangents to the curve y=\frac{x+2}{3x+4} with a positive slope.

    How would I solve this? All help appreciated!
    Last edited by mr fantastic; February 15th 2011 at 05:34 PM. Reason: Re-titled.
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    Quote Originally Posted by youngb11 View Post
    Show that there are no tangents to the curve y=\frac{x+2}{3x+4} with a positive slope.

    How would I solve this? All help appreciated!
    Calculate the numerator of the derivative with the Quotient Rule
    and show that it cannot be >0

    (the denominator of the derivative is a square)

    v\frac{du}{dx}-u\frac{dv}{dx}=(3x+4)-3(x+2)
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    Quote Originally Posted by Archie Meade View Post
    Calculate the numerator of the derivative with the Quotient Rule
    and show that it cannot be >0

    (the denominator of the derivative is a square)

    v\frac{du}{dx}-u\frac{dv}{dx}=(3x+4)-3(x+2)
    Numerator worked out to be -2. Any tips on how you would show it (format) if you were doing it? Thanks again!
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    The derivative gives you the slope of the tangent, in terms of x.
    Since the denominator is a square, it's positive.
    Then, since the numerator is free of x and negative, the derivative is always negative,
    which means that all tangents have negative slopes
    (no tangent has a positive slope).
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