calculus

posted by .

A rectangle with its base on the x-axis is to be inscribed under the graph of y=2-x^2. Find the height of the rectangle if the area is the largest possible area.

  • calculus -

    let the point of contact of the rectangle with the parabola in the first quadrant be P(x,y)
    So the base of the rectangle is 2x and its height is y
    Area = 2xy
    = 2x(2-x^2)
    = 4x = 2x^3
    d(Area)/dx = 4 - 6x^2 = 0 for a max/min of area

    6x^2 = 4
    x = √(2/3)

    then the height for a max area
    = 2 - 2/3
    = 4/3

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    I have to find the area of the largest possible rectangle that can be inscribed under the curve y=e^(-x^2) in the first and second quadrants. How do I do this?
  2. 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?
  3. 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?
  4. 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?
  5. Calculus

    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?
  6. math analysis

    A rectangle with its base on the x axis is to be inscribed under the positive portions of the graph of y=8-x^2 . Write an equation for the area of the rectangle which uses only the variable x.
  7. calculus

    A rectangle with its base on the x-axis is to be inscribed under the graph of y=2-x^2. Find the height of the rectangle if the area is the largest possible area. (Round to the nearest hundreth)
  8. Calculus

    Hello, could someone please help me with this problem?
  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