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!

Inscribed area

  1. Jan 4, 2008 #1
    Find the area of the largest rectangle that can be inscribed in the region bounded by the parabola with equation y= 4 - x^2
  2. jcsd
  3. Jan 4, 2008 #2


    User Avatar
    Science Advisor

    I find it difficult to believe that this is not homework and so belongs in the "homework section". I will move it. Also you are expected to show what you have tried.

    Are you allowed to assume that the rectangle has horizontal and vertical sides? It can be proved that the largest rectangle must be that way butnot so easy to prove.

    Assuming that, take one vertex at (x0,0) (Since it is inscribed in the figure, if one side is horizontal, two vertices must be on the x-axis). It should be easy to see by symmetry that the other vertex must be (-x0, 0). Do you see that the "upper" vertices then are at (x0, 4-x02) and (x0, 4- x02)?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook