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Minimum d occurs at minimum d^2

  1. Jan 18, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the point on the parabola y^2 = 2x that is closest to the point (1,4)

    2. Relevant equations
    d = ((x-1)^2 + (y-4)^2)^1/2
    3. The attempt at a solution
    My attempt involves subbing in x in the d equation and differentiating it. I cant get the same answer as the book because they differentiate d^2 = not d = to make it easier to solve.
    They state "you should convince yourself the minimum of d occurs at the same point as the minimum of d^2, but d^2 is easier to work with"

    How do i know it occurs at the same point?
    Last edited by a moderator: Jan 18, 2016
  2. jcsd
  3. Jan 18, 2016 #2


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    Try to find positive ##d_1 < d_2## with ##d_1^2 > d_2^2##
  4. Jan 18, 2016 #3


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    If ##0<a<b## then ##a\cdot a < a \cdot b < b\cdot b##.
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