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Thread: Derivative of function

  1. #1
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    Post Derivative of function- tangent/normal

    $\displaystyle y = \frac{3x+4}{x-1}$

    a. Determine all values for $\displaystyle x$ for which $\displaystyle \frac{dy}{dx}$ exists.

    b. Find an expression for $\displaystyle \frac{dy}{dx}$.


    Here are my answers..are they correct?

    a. All real numbers not equal to 1

    b. $\displaystyle \frac{-5}{(x-1)^2}$
    Last edited by live_laugh_luv27; Oct 25th 2009 at 10:52 AM.
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  2. #2
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    Quote Originally Posted by live_laugh_luv27 View Post
    $\displaystyle y = \frac{3x+4}{x-1}$

    a. Determine all values for $\displaystyle x$ for which $\displaystyle \frac{dy}{dx}$ exists.

    b. Find an expression for $\displaystyle \frac{dy}{dx}$.


    Here are my answers..are they correct?

    a. All real numbers not equal to 1

    b. $\displaystyle \frac{-5}{(x-1)^2}$

    a) Correct.

    b) Incorrect. Should actually be $\displaystyle -\frac{7}{(x - 1)^2}$.
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  3. #3
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    Post

    ok, thanks.
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  4. #4
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    2 additional questions:

    1) Find line tangent to the curve at $\displaystyle (8,4)$

    2) Find line normal to the curve at $\displaystyle (8,4) $and determine the cooridinates of another point where this line intersects the graph.

    Here is what I came up with:

    1) $\displaystyle y-4=-\frac{7}{64}(x-8)$

    2) $\displaystyle y-4=\frac{64}{7}(x-8)
    $
    Is this correct? I'm unsure what the second part of the second question is asking. Any help is appreciated.
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