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A rectangle is inscribed with its base on the -axis and its upper corners on the parabola y = 7 - x ^ 2 What are the dimensions of such a rectangle with the greatest possible area?

A Rectangle Is Inscribed With Its Base On The Axis And Its Upper Corners On The Parabola Y 7 X 2 What Are The Dimensions Of Such A Rectangle With The Greatest P class=

Sagot :

Answer:

The width = 3.06

The height = 4.66

Explanation:

The rectangle is inscribed with its base on the -axis and its upper corners on the parabola

Width = 2x

Height = 7 - x²

Area of the inscribed rectangle:

Area = width x height

A = 2x (7 - x²)

A = 14x - 2x³

Take the derivative of the area (A) and equate to zero

A' = 14 - 6x²

0 = 14 - 6x²

6x² = 14

x² = 14/6

x² = 2.33

x = √2.33

x = 1.53

The width = 2x

The width = 2(1.53)

The width = 3.06

Substitute x = 1.53 into the equation y = 7 - x² to solve for the height

y = 7 - 1.53²

y = 4.66

The height = 4.66

View image ZamirL483593
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