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Math Help - Determine the general equation of the secant from any point - Help!

  1. #1
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    Determine the general equation of the secant from any point - Help!

    I have to find the general equation of a secant from any point (A,f(A)) to the point on f(x) =  4^x where x = 2. That point is (2,16) Can someone help me develop this equation. I have an example. But they use the point (4,4) so its hard to tell what is the x and what is the y and how they are expanded and everything.
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  2. #2
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    Equation of a line through a point (h,k) and with a given slope "m" is given by

    (y-k) = m (x-h)

    ------------------------------

    Slope of a tangent at any point h on 4^x is given using differentiation of f(x)..

    f(x) = 4^x

    f'(x) = 4^x ln(4)

    So

    f'(h) = 4^h \cdot ln(4)

    Hence the value of m in your question at any point (h,k) " lying on the curve": is

    m = 4^h \cdot ln(4)


    -----------

    So equation of tangent is

     (y-k) =  4^h \cdot ln(4) \cdot (x-h)

    --------------------

    (h,k) is ( 2,16) in this particular problem.

    Still in trouble feel free to ask.
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