Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

Optimization Problem?

A rectangle is inscribed between two parabolas y=4x^2 and y=30-x^2. What is the area of the largest rectangle that could be inscribed?

Please Help! I have no clue.

1 Answer

Relevance
  • 1 decade ago
    Favorite Answer

    Find where they intersect to find the bounds on the width

    4x² = 30 - x²

    5x² = 30

    x² = 6

    x = ±√6

    So the width must be between 0 and 2√6 (exclusive) and is given by the function 2x. The height of the rectangle is given by the difference of the functions, larger minus smaller.

    h = 30 - x² - 4x² = 30 - 5x²

    A = hw = (30-5x²)(2x) = 60x - 10x³

    A' = 60 - 30x² = 0 ⇒ x = ±√2 ⇒ x = √2

    w = 2√2

    h = 20

    A = 40√2 ≈ 56.569

    The key to this whole thing is graphing the 2 equations and trying to visualize an inscribed rectangle.

    Pic: http://i448.photobucket.com/albums/qq205/_dot_math...

Still have questions? Get your answers by asking now.