1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    x=y^2/2
    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

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

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

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If ##0<a<b## then ##a\cdot a < a \cdot b < b\cdot b##.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Minimum d occurs at minimum d^2
Loading...