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Normals to Curves (Differentiation)

  1. Apr 21, 2010 #1
    Hi there
    If possible can someone please review my understanding of this question.

    1. The problem statement, all variables and given/known data

    At what point on the Parabola y= 2x^2-7x-15 will a normal to the parabola have a gradient of -1/2

    2. Relevant equations


    3. The attempt at a solution

    We are given the gradient of the normal as -1/2
    Therefore gradient of the tangent = 2

    dy/dx = 4x - 7 = 2
    4x = 9
    x = 2.25 (2 1/4)

    plug into y = 2(2.25)^2 - 7(2.25) - 15
    y = -20 5/8

    Therefore the point on the parabola - where a normal to the parabola will have a gradient of
    -1/2 = (2 1/4, -20 5/8).
     
  2. jcsd
  3. Apr 21, 2010 #2

    tiny-tim

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    Hi zebra1707! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    Looks good! :smile:
     
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