Algebra II

Find the difference quotient for the following Rational Function f(x)=5/x using the four steps outlined below.
a. find f(x+h)
b. find f(x)
c. substitute f(x+h) and f(x) into the difference quotient formula.
d. simplify

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  1. f(x+h) = 5/(x+h)
    f(x) = 5/x

    [f(x+h) - f(x)]/h = [5x -5(x+h)]/[hx(x+h)]

    = -5 /[x(x+h) }

    = -5/(x^2+hx)

    By the way,
    if you take the limit of that as h--->0
    then you are a calculus student and you just found the derivative
    d/dx (5/x) = -5/x^2

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    posted by Damon

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