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?

  1. 👍
  2. 👎
  3. 👁
  1. Consider half of the rectangle which lies completely in the first quadrant.
    The lower left corner is the origin (0,0), and the upper right corner lies on the curve y=9-x².

    The area of the (half) rectangle is therefore:

    A(x)
    =x*y
    =x*(9-x²)
    =9x-x³

    Differentiate with respect to x,
    and equate A'(x) to zero to get the value of x that will result in the maximum area. The area of the required rectangle is twice A(x) because the other half of the rectangle is in the second quadrant.

    Do check that A"(x)<0 to confirm that the area is a maximum (and not a minimum).

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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? Find Width=____ & Height=4 just need to find

  2. 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)

  3. AP Calculus

    A rectangle is inscribed between the parabolas y=4x^2 and y=30-x^2. what is the maximum area of such a rectangle? a)20root2 b)40 c)30root2 d)50 e)40root2

  4. math

    Rectangle ABCD is dilated to form rectangle A’B’C’D’. What is the dilation factor? What is the center of dilation? Select all that apply. The figure shows two rectangles UpperWord ABCD and UpperWord A complement, B

  1. algebra

    What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 27 - x2

  2. Calculus

    Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola y=4−x^2. Width = Height =

  3. calculus

    A rectangle has its base on the x-axis and its 2 upper corners on the parabola y=12-x^2. What is the largest possible area of the rectangle?

  4. calculus- optimization

    A rectangle is inscribed into a semi circle at radius 2. What is the largest area it can have and what are the dimensions Answers Area= 4 max base =2sqrt2 height = sqrt2 Help is always appreciated :)

  1. Calculus

    A rectangle is inscribed in a semicircle with radius 8. The variable x is half the length of the rectangle. Write an expressions for the perimeter and area of the rectangle in terms of x.

  2. calculus

    a rectangle has its base on the x-axis, and its upper corners in the graph of y=27-x^2. what is the maximal area of this rectangle?

  3. Calculus

    A rectangle has one corner in quadrant I on the graph of y = 9 − x^2,another corner at the origin, and corners on both the positive y-axis and the positive x-axis. As the corner on y = 9 − x2 changes, a variety of rectangles

  4. Calc

    A rectangle is to be inscribed in a semicircle of radius 8, with one side lying on the diameter of the circle. What is the maximum possible area of the rectangle?

You can view more similar questions or ask a new question.