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Sagot :
A rectangle's greatest area is 32 square units.
Given:
A parabola's equation is y = 12 - x2, which is an even function
As a result, its rectangular shape is also even at the origin.
We are aware that the area of a rectangle is equal to its length times its width.
Here,
width = y, length = 2x
A = 2x, where (12 - [tex]x^{2}[/tex])
⇒ A = 24x - 2[tex]x^{3}[/tex]
Consider the A derivative with regard to x.
⇒ A' = 24 - 6 [tex]x^{2}[/tex]
When A' = 0, the area is the largest.
⇒ 24 - 6x2 = 0
⇒ [tex]x^{2}[/tex] = 4
⇒ x = 2
Replace x with its value in y = 12 - [tex]x^{2}[/tex].
⇒ y = 12 - 4
⇒ y = 8
Area = 2(2)(8) = 32
Hence, a rectangle's greatest area is 32 square units.
To learn more about function:
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