Results 1 to 2 of 2

Math Help - Calculus - maximizing area

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    2

    Calculus - maximizing area

    A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 10−x2. What are the dimensions of such a rectangle with the greatest possible area?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Dec 2008
    Posts
    319
    We first formulate everything in mathematical terms: if x is the distance from the origin of one lower corner of the rectangle, then the base of the rectangle is 2x, and the height of the rectangle is 10-x^2. Its area is therefore

    A=2x\cdot(10-x^2).

    To maximize A, we remember that A is differentiable everywhere and approaches 0 at the boundary points of its domain, and therefore that A will attain an extremum at some point at which \frac{dA}{dx}=0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Maximizing Area.
    Posted in the Pre-Calculus Forum
    Replies: 14
    Last Post: January 27th 2010, 08:43 PM
  2. Calculus Maximizing and Integrals
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 10th 2009, 04:25 AM
  3. Maximizing Area
    Posted in the Calculus Forum
    Replies: 7
    Last Post: September 18th 2008, 03:33 AM
  4. Maximizing Area & Differentials
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 16th 2007, 10:18 PM
  5. Maximizing Area
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 28th 2007, 10:03 AM

Search Tags


/mathhelpforum @mathhelpforum