Results 1 to 4 of 4

Math Help - Maximum Area (optimization)

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    229

    Maximum Area (optimization)

    A rectangle is bounded by the x-axis and the semicircle
    y = sqrt(25 - x^2)
    What length and width should the rectangle have so that its area is a maximum?

    I end up with A' = (-2x^2 + 25) / (25 - x^2)^1/2. Am I on the right track or did I make a terrible mistake?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by Archduke01 View Post
    A rectangle is bounded by the x-axis and the semicircle
    y = sqrt(25 - x^2)
    What length and width should the rectangle have so that its area is a maximum?

    I end up with A' = (-2x^2 + 25) / (25 - x^2)^1/2. Am I on the right track or did I make a terrible mistake?
    You're on the right track...

    However, I get

    A'(x)=\frac{2(25-x^2)}{\sqrt{25-x^2}}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2009
    Posts
    229
    Quote Originally Posted by VonNemo19 View Post
    You're on the right track...
    So I made A' equal to zero and... got stuck. I don't know how to proceed from there and isolate x^2. Any help would be appreciated.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by Archduke01 View Post
    So I made A' equal to zero and... got stuck. I don't know how to proceed from there and isolate x^2. Any help would be appreciated.

    A'(x)=0\Rightarrow25-2x^2=0

    x^2=\frac{25}{2}

    \Rightarrow{x}=\frac{5\sqrt2}{2}

    This makes good sense because you would expect the greatest area to be given when the diagonal in the first quadrant makes an angle of \theta=\pi/4 with the x-axis. And the cosine of \pi/4 is...

    \sqrt{2}/2.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: May 9th 2010, 04:05 AM
  2. Maximum Area
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 3rd 2010, 03:52 PM
  3. Optimization problems(maximum and minim.)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 1st 2009, 07:02 AM
  4. Maximum Area
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 5th 2009, 06:25 PM
  5. maximum area
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 18th 2006, 03:09 PM

Search Tags


/mathhelpforum @mathhelpforum