SOLUTION: This time rectangle R has varying length l and width w but with a constant area of 4 square feet. a) Express the perimeter P as a function of length l What type of function is P

Question 894730: This time rectangle R has varying length l and width w but with a constant area of 4 square feet.
a)
Express the perimeter P as a function of length l
What type of function is P? What is the domain of P?
b)Describe the asymptotic behavior of P. What can you say about rectangle R because of this behavior? Could you have made a similar statement about R back in Task 1?
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 josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
l is a bad choice for length. Choose L for length.

A is area and is constant A=4.
; perimeter p is .
allows for .

Domain for p is .

Knowing that A=4,

Further,

This is a rational function, and there is an asymptote for L=0.
L^2 becomes smaller faster than L, as L approaches 0, but looking at the separate terms 8/L and 2L^2/L, seeing 8/L increases while 2L^2/L will decrease without bound as L approaches 0. The function p of L will increase without bound as L approaches 0.

You might try derivative and look for the local minimum, but the graph shows a minimum perimeter at about L=2.

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