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Tangent lines parallel

  1. May 5, 2013 #1
    1. The problem statement, all variables and given/known data
    The line x-2y+9=0 is tangent to the graph of y=f(x) at (3,6) and is also parallel to the line through (1,f(1)) and (5,f(5)). If f is differentiable on the closed interval [1,5] and f(1)=2, find f(5)

    A) 2
    B) 3
    C) 4
    D) 5
    E) None of these

    The correct answer is (C) 4


    3. The attempt at a solution

    So I know the tangent line to (3,6) and f(5) have the same slope:

    x-2y+9=0
    2y=x+9
    y=.5x+4.5

    So, the slope is .5 at f(1), f(3), and f(5)

    Now, I need to find the point at f(5). I do not know how to do this
     
  2. jcsd
  3. May 5, 2013 #2
    1) The slope of the first line is 1/2

    2) The slope of the line is passing through (1,2) and (5, f(5)). Then use the definition of slope:

    [tex]1/2=\frac{f(5)-2}{5-1}[/tex]

    and solve for f(5).
     
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