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Math Help - Difference Quotient

  1. #1
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    Difference Quotient

    I am new here but I have a question about this difference quotient. Hope you can help me!

    f(x)=√5x
    f(x)-f(5)/x-5

    didn't know how to show it but f(x)-f(5) are all over x-5
    So thank you if you can help me figure this out! I know the answer but I am not sure how to get to it....
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  2. #2
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    Quote Originally Posted by TimelordGurl View Post
    I am new here but I have a question about this difference quotient. Hope you can help me!

    f(x)=√5x
    f(x)-f(5)/x-5

    didn't know how to show it but f(x)-f(5) are all over x-5
    So thank you if you can help me figure this out! I know the answer but I am not sure how to get to it....
    Okay, so this is \frac{f(x)- f(5)}{x-5}. Now replace "f(x)" and "f(5)" by this specific function.

    But is f(x)= (\sqrt{5})x or is f(x)= \sqrt{5x}?

    If the first, \frac{f(x)- f(5)}{x-5}= \frac{(\sqrt{5}x- \sqrt{5}}{x-5} = \frac{\sqrt{5}(x-5)}{x-5}= \sqrt{5}.
    (Which you should have expected- y= (\sqrt{5})x is a linear function with slope \sqrt{5}.)

    If the second, frac{f(x)- f(5)}{x-5}= \frac{\sqrt{5x}- \sqrt{5}}{x-5} which is harder to simplify. Try multiplying both numerator and denominator by \sqrt{5x}+\sqrt{5}.
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