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Math Help - line, function, moving tangency

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    line, function, moving tangency

    Given the line y=-\frac{k}{m}x+k, where k is the y axis intercept and m is the x axis intercept, and the function y=f(x), where f(x)=\frac{1}{x-1}, find a formula for the scalar a such that af(\frac{x}{a}) is always tangent to the line y=-\frac{k}{m}x+k for any positive real k and m.

    See the attached graph for an illustration. In plain English the question is: if the line moves, what do you have to do to "a" so that af(x/a) is still tangent to the line.

    I will now send my answer to the moderators.

    Moderator approved CB
    Attached Thumbnails Attached Thumbnails line, function, moving tangency-clipboard01.jpg  
    Last edited by CaptainBlack; November 14th 2010 at 03:06 PM.
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