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!

Optimization of Area; Inscribed Rectangles

  1. Nov 4, 2013 #1

    Qube

    User Avatar
    Gold Member

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

    http://i.minus.com/jbkHm5oH1LfQ1k.png [Broken]

    2. Relevant equations

    The area of a rectangle is its base times its height.

    3. The attempt at a solution

    The rectangle is inscribed. Its area is 2xy. I can substitute in the equation of the semicircle to get rid of the y-term in my area equation. I can then differentiate with respect to x and find what zeros the derivative (or causes the derivative not to exist) and test the points I find that are on the domain of x (0 to square root of 12).

    I find x = sqrt6 as that point that maximizes area and therefore the dimensions must be 2sqrt6 and sqrt6.

    http://i.minus.com/jFWGaWoQsb5FX.jpg [Broken]
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Nov 4, 2013 #2

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Looks right to me.
     
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: Optimization of Area; Inscribed Rectangles
  1. Inscribed area (Replies: 1)

Loading...