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Homework Help: Calculus, again

  1. Feb 27, 2005 #1
    Consider the pababola y=x^2+bx+c. Find the values of b and c such that the line y=2x is tangent to the point (2,4).

    I've no clue at all...
  2. jcsd
  3. Feb 27, 2005 #2


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    Really, no clue at all? Did it not occur to you that if the line is tangent to the parabola at the point (2,4), then the parabola must go through (2,4)- that is, that
    4= 22+ b(2)+ c.

    Has no one told you that the derivative at a point IS the slope of the tangent line at that point? What is the slope of the line y= 2x? Can you find the derivative of
    y= x2+ bx+ c at x= 2?
  4. Feb 27, 2005 #3
    You have y = 2x as the tangent line.. and you know that y' = 2x + b and thus you can substitute x = 2 into y' to get y' = 4 + b and from the question you know y' = 2... and so 2 = 4 + b; b = -2
    Next step is finding c, just plug in:
    4 = 4 - 4 + c
    c = 4
    And the parabola is y = x^2 - 2x + 4
    And to test it..
    y' = 2x - 2
    And at the point (2,4); y - 4 = 2(x-2); y = 2x - 4 + 4 = 2x
    And that's the answer...
    Or I could be completely wrong. :approve:
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