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Homework Help: Tangent line through arbitrary point?

  1. Oct 12, 2011 #1
    1. The problem statement, all variables and given/known data

    Consider the function f(x)=x2+5x+5 and the point A(4,5).

    Find a formula for the slope of a line passing through point A, and an arbitrary point on the function. Your answer should be a formula in terms of x.
    slope=???

    2. Relevant equations

    f′(x)=2x+5

    3. The attempt at a solution

    Using your answers from the two previous questions, find the slope(s) of the line(s) through point A that is (are) tangent to f(x)

    the slopes are 1, and 25 however I don't understand what part two of the question is asking for...
    (formula for slope passing through point A, and arbitrary point on the function)
     
  2. jcsd
  3. Oct 12, 2011 #2

    Mark44

    Staff: Mentor

    First off, your thread title seems misleading to me, as this problem has nothing to do with tangent lines. All they are asking for is the slope of a line that goes through A(4, 5) and an arbitrary point on the graph of y = x2 + 4x + 5. Note that A is not on the graph of this parabola.

    The question boils down to finding the slope of the line through two points: A(4, 5) and some point on the graph of the parabola. What are the coordinates of each point on the parabola?
     
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