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Finding tangent line

  1. Oct 17, 2013 #1
    1. If an equation of the tangent line to the curve y=f(x) at the
    point a=2 where is y=4x-5, find f(2) and f'(2).



    2. Relevant equations

    m=[itex]\frac{f(x)-f(a)}{x-a}[/itex]

    3. The attempt at a solution

    To be honest, I really don't know where to start. Here's what I have so far:

    m=[itex]\frac{f(x)-f(a)}{x-a}[/itex]

    I know slope is 4 according to the equation above. Also, I know there is a point (2,3), plugging a into the equation.

    4=[itex]\frac{f(x)-3)}{x-2}[/itex]

    Now what can I do? This doesn't help me find f(2) or f'(2).

    Any help would be greatly appreciated.
     
  2. jcsd
  3. Oct 17, 2013 #2

    jbunniii

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    What is the relationship between the slope of the tangent line and the derivative?
     
  4. Oct 17, 2013 #3
    The slope -is- the derivative.
     
  5. Oct 17, 2013 #4

    jbunniii

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    OK, good. So you established that the slope of the tangent line at the point ##x=2## is ##4##. What does that tell you about ##f'(2)##?
     
  6. Oct 17, 2013 #5
    I got it! Thanks!

    f'(2) = 4 and f(2) = 3!
     
  7. Oct 17, 2013 #6
  8. Oct 17, 2013 #7

    jbunniii

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    Looks good. I'll take a look at your other question now.
     
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