# 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)

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. Let the point of contact of the rectangle in the first quadrant be (x,y)

then the base of the rectangle is 2x and the height is y
Area = 2xy
= 2x(2-x^2)
= 4x - 2x^3
d(Area)/dx = 4 - 6x^2
= 0 for a max of Area
6x^2 = 4
x^2 = 4/6
x = ±2/6
then height = y = 2 - 4/6 = 4/3
= 1.33 to the nearest hundreth

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### geometry

In the graph below, point D is reflected across the y-axis. What are the coordinates of it's image? The graph looks like D is below the x-axis to the right 3 places from y-axis and down 1 place from x-axis. So would my answer be

2. ### Calculus AP

Let R be the region in the first quadrant bounded by the graph y=3-√x the horizontal line y=1, and the y-axis as shown in the figure to the right. Please show all work. 1. Find the area of R 2. Write but do not evaluate, an

3. ### calculus

The base of a solid is the region in the first quadrant bounded by the graph of y = 3/(e^x) , the x-axis, the y-axis, and the line x=2. Each cross section of this solid perpendicular to the x-axis is a square. What is the volume

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. ### 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

2. ### 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?

3. ### alg 2

a rectangle is to be inscribed in a isosceles triangle of height 8 and base 10. Find the greatest area of such rectangle.

4. ### Calculus

Find the area of the largest rectangle having one side on the x-axis and inscribed in a triangle formed by the lines y=x, y=0 and 3x+y=20.

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

The graph of f'(x) is shown for 0=< x =

3. ### Math

Find the maximum area of a rectangle inscribed in the region bounded by the graph of y = (3-x)/(2+x) and the axes. (Round your answer to four decimal places.)

4. ### 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?