# Area Problem

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• October 18th 2007, 05:12 PM
cdoubleokay
Area Problem
If 300 feet of fence are used to enclose a rectangular pen, the resulting area of the pen is A=150x-x^2, where x is the width of the pen.

a.What should the width be in order to have the max area?

b.What is the maximum possible area?
• October 18th 2007, 08:12 PM
earboth
Quote:

Originally Posted by cdoubleokay
If 300 feet of fence are used to enclose a rectangular pen, the resulting area of the pen is A=150x-x^2, where x is the width of the pen.

a.What should the width be in order to have the max area?

b.What is the maximum possible area?

Hello,

to a.): You get the extreme value of A(x) if the first derivative of A equals zero.
Calculate A'(x).
Solve the equation A'(x) = 0 for x. (For confirmation only: x = 0 or x = 75)

to b.): Plug in the result from a.) into the given equation of the function. Determine which of the 2 values is the maximum :D (for confirmation only: $A_{max} = 5625$)