1. Limited time only! Sign up for a free 30min personal 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!

Find min/max distance between (0,4) and y=x^2/4

  1. Dec 9, 2009 #1
    I am trying to find the minimum and maximum distance between point (0,4) and the line y=(x^2)/4 in the region of 0<=x<=2√3.

    This is what i have so far

    y(distance)=√((x-0)^2+((x^2)/4)^2)
    =(x^2+(X^4)/16+16)^0.5
    then calculate y'
    then make y'=0
    then determine if max or min using 2nd derivative test

    The problem i am having is that the answers i get for x when y' = 0 are imaginary. i have computed this problem using matlab and get the same answers except that they are real and have isolated the problem to my simplification of y.

    matlab gives it as y=0.25(-16x^2+x^4+256)^0.5

    Could some one please explain how to simplify y=(x^2+(X^4)/16+16)^0.5 to y=0.25(-16x^2+x^4+256)^0.5 or suggest a better way to approach this problem

    Thanks in advance
     
  2. jcsd
  3. Dec 9, 2009 #2

    ideasrule

    User Avatar
    Homework Helper

    I think you meant [(x^2)/4-4]^2, not [(x^2)/4]^2. Also, you might find it easier to calculate the derivative of y^2 instead of y. Squaring the distance eliminates the square root, which is a major pain in the neck.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook