# The area of a rectangle can be modeled by A = b (4-b ), where A is the area of the rectangle, and b is the length of the base (in inches). ?

What is the greatest possible area of the rectangle?

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- Pramod KumarLv 71 month ago
A = b ( 4 - b ) = 4 b - b²

dA/db = 4 - 2 b

For maximum Area, dA/db = 0

=> 4 - 2 b = 0

=> b = 2

Then A will be equal to --

A = 2 ( 4 - 2 ) = 4 sqr inch ................. Answer

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- MichaelLv 71 month ago
A = b (4 - b)

A = 4b - b²

This is a parabola

-b² + 4b - A = 0

Since the coefficient of b² is negative the parabola opens down

and the vertex is a maximum

The roots are

b = 0

(4 - b) = 0 ===> b = 4

b = {0, 4}

-------------------------

the vertex occurs at the midpoint of the roots

b = (0 + 4) / 2

b = 2

The maximum will be

A = 2(4 - 2)

A = 2 * 2

A = 4 in² <–––––

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