Calculus

posted by .

A rectangle is inscribed with its base on the x -axis and its upper corners on the parabola
y= 11-x^2.

What are the dimensions of such a rectangle with the greatest possible area?

  • Calculus -

    The area of the rectangle with corners (-x,0), (x,0) (-x,y) (x,y) is

    a = 2x * (11-x^2)
    a = 22x - 2x^3

    da/dx = 22 - 6x^2
    da/dx = 0 when x = √(11/3)

    So, the rectangle is 2√(11/3) x 22/3 with area 44/3 * √(11/3) = 28.08

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=9-x^2. What are the dimensions of such a rectangle with the greatest possible area?
  2. Calc

    A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 1-x^2. What are the dimensions of such a rectangle with the greatest possible area?
  3. Calculus

    A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=2-x^2 What are the dimensions of such a rectangle with the greatest possible area?
  4. CALC

    A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=9–x2. What are the dimensions of such a rectangle with the greatest possible area?
  5. CALC

    A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=9–x2. What are the dimensions of such a rectangle with the greatest possible area?
  6. calculus

    A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=12−x2. What are the dimensions of such a rectangle with the greatest possible area?
  7. Calculus

    A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y= 12 - x^2. What are the dimensions of such a rectangle with the greatest possible area?
  8. Calc Help Please

    A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola f(x)=8-x^2. What are the dimensions of such a rectangle with the greatest possible area?
  9. Calculus

    A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=4−x^2. What are the dimensions of such a rectangle with the greatest possible area?
  10. Calculus

    A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 6-x^2. What are the dimensions of such a rectangle with the greatest possible area?

More Similar Questions