1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Determine the equation of the tangent line

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

    [itex]\frac{3x+6}{2-x}[/itex]

    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

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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

    [itex]\frac{f(x+h)-f(x)}{h}[/itex]

    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

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Determine the equation of the tangent line
  1. Equation of Tangent Line (Replies: 14)

Loading...