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Calculus/Rectangular Pen Problem
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Question
A rectangular pen is built against a wall so that only three sides will require fencing. If f fet of fencing are to be used , the area of the largest possible pen in square feet is?
I set the problem up this way. Is my answer correct?
y= f-2x
A= x(f-2x)
A=(xf-2x^2)
A'(x)= f+x-4x x=f/3 Area= f/3 x f/3= f^2/9
For the variables, y is the length, x is the width, f is the total fencing, and A is the area.
The area A is the length times the width, which I see.
The derivative of A with respect to x (remembering the f is a constant) is f - 4x.
This means that x = f/4 (again, f is a constant).
Put this value back into A = x(f-2x) and you will have the area.
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Answers by Expert:
Scotto
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