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!

Homework Help: Maximum and minimun problem

  1. May 21, 2006 #1
    1. Find the dimensions of the rectangle with largest area which can be cut from a circle with equation x^2+ y^2= 4

    this is the question but i got stuck half way when i was differentiating the equation

    how do i work this out :
    [square root of (4-y^2)] + ([-y ^2] \ square root[ 4- y^2])
  2. jcsd
  3. May 21, 2006 #2
    So if A represents the area of the rectangle, you have [tex]\frac{dA}{dy}=4(\frac{-y^2}{\sqrt{4-y^2}}+\sqrt{4-y^2})[/tex].

    If you observe the expression, is there something you can factorize that will make it easier to solve for y when you set [tex]\frac{dA}{dy}=0[/tex]?
  4. May 21, 2006 #3
    Actually, from symmetry you can argue that the required rectangle has to be a square (special case of a rectangle) whose diagonals meet at the centre of the circle of radius 2 units .
    What can you say about the length of the side of this square ?
    Hint:Draw radii to the corners of the square .

    Of course if the symmetry isn't apparent, you can always go for the calculus approach, which involves setting up coordinate axes and maximising .
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook