Results 1 to 2 of 2

Math Help - Finding the largest area??

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    126

    Finding the largest area??

    A rectangle is inscribed in the semicircle y = sqrt[4 - x^2]. Find its largest possible area.

    I think I am suppose to take the derivative, but what do I do next??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Like a stone-audioslave ADARSH's Avatar
    Joined
    Aug 2008
    From
    India
    Posts
    726
    Thanks
    2
    Quote Originally Posted by elpermic View Post
    A rectangle is inscribed in the semicircle y = sqrt[4 - x^2]. Find its largest possible area.

    I think I am suppose to take the derivative, but what do I do next??
    Center of the circle was (0,0)

    We take a point (x,0) as one of the edge of rectangle

    The edge just above (x,0) will have
    y coordinate lying on the semicircle and given by

    \sqrt{4-x^2} , hence its coordinate is

    (x , \sqrt{4-x^2})

    --------------------------------
    Make sure you get the above part before you continue.
    ---------------------------------


    Area of this rectangle will be given by

    = 2x \times (\sqrt{4-x^2})

    ...............{2 times of x because the length will lie on both side of the axis}

    ------------------------
    if you don't get the above thing try drawing the diagram.
    -------------------------------


    This area needs to be max. so try finding the maximum
    value of Area(x)


    A(x) = 2x\sqrt{4-x^2}

    for maxima

    <br />
\frac{d}{dx}A(x) = 0

    From above get the value of x for which A(x) is 0 . try this

    value on A(x) to get max. area.


    --------------------------
    Be sincere enough to read below after you have solved.

    Spoiler:

    <br />
\frac{d}{dx} 2x \sqrt{4-x^2} = 0

    <br />
2\sqrt{4-x^2}+\frac{-x^2}{\sqrt{4-x^2}} = 0

    2(4-x^2) =x^2

    <br />
8 = 3x^2

    <br />
x=\pm \sqrt{\frac{8}{3}}



    Now find area(use +ve x).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Showing that a square has largest area
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: July 7th 2010, 10:27 PM
  2. Replies: 3
    Last Post: May 5th 2009, 09:29 AM
  3. largest area geometry
    Posted in the Geometry Forum
    Replies: 4
    Last Post: June 29th 2008, 01:56 AM
  4. Find rectangle with largest area
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 21st 2008, 05:22 PM
  5. largest area
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 27th 2007, 07:46 AM

Search Tags


/mathhelpforum @mathhelpforum