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Homework Help: Determine the equation of the tangent line

  1. Oct 6, 2012 #1
    1. The problem statement, all variables and given/known data


    at [itex]x=3[/itex]

    2. Relevant equations

    y - y[itex]_{o}[/itex] = m(x-x[itex]_{o}[/itex])

    3. The attempt at a solution

    f(3) = -[itex]\frac{15}{4}[/itex]

    m = [itex]\frac{3}{0}[/itex] DNE

    I have to write the equation in the form of the point-slope formula.

    I can get x[itex]_{o}[/itex] and y[itex]_{o}[/itex], but I am having trouble finding m.

    Thanks for any help.
  2. jcsd
  3. Oct 6, 2012 #2


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    You didn't give an equation. I suppose it is$$
    y=\frac{3x+6}{2-x}$$You need to calculate its derivative at ##3## to get the slope. You might also check your ##f(3)##.
  4. Oct 6, 2012 #3
    Sorry, yes that is the equation. Can you help me find the derivative? I'm a bit confused because my textbook says that the derivative is


    but in class we learned that as the difference quotient, and that the derivative is when you do this:

    y = x[itex]^{n}[/itex]
    y' = nx[itex]^{n-1}[/itex]

    Thanks for the fast reply
  5. Oct 6, 2012 #4


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    That is not the derivative of f(x). You have to take the limit as ##h \to 0## to get the derivative.
    That gives the rule for differentiating powers, which is derived from the difference quotient by letting ##h\rightarrow 0##. For more complicated derivatives like your quotient, you would use the quotient rule and the power rule. Haven't you had the quotient rule?
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