SOLUTION: Rectangle R has varying length L and width Wbut a constant area of 4ft^2 A: Express the perimeter P as a function of l and what kind of function is P? wahat is its domain? B:

Algebra ->  Rational-functions -> SOLUTION: Rectangle R has varying length L and width Wbut a constant area of 4ft^2 A: Express the perimeter P as a function of l and what kind of function is P? wahat is its domain? B:      Log On


   

Question 1038672: Rectangle R has varying length L and width Wbut a constant area of 4ft^2
A: Express the perimeter P as a function of l and what kind of function is P? wahat is its domain?
B:Describe the asymptotic behavior of P. What can you say about rectangle R because of this behavior?
c:For what values of l and w will the perimeter of R be the least?
Give a geometric explanation. Be sure to include a graph with relevant points labeled.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A=L%2AW=4
L=4%2FW
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A: P=2L%2B2W=2%28L%2BW%29=2%284%2FW%2BW%29
The width cannot be less than zero but can be as large as you wish so then the perimeter is the same type of function.
It cannot be less than zero but it can be as large as you wish.
W%3E0
L%3E0
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B: As W gets large, 4%2FW-%3E0, so then P looks like a linear function of W
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C: P=2%284%2FW%2BW%29
Since it's a function of one variable, you can find the derivative to get the minimum value,
dP%2FdW=-8%2FW%5E2%2B2
%28-8%2FW%5E2%29%2B2=0
-8%2FW%5E2=-2
W%5E2=4
W=2
So then,
L=4%2F2
L=2
So the minimum perimeter would be,
P=2%282%2B2%29=8ft