Question

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 1

Here is what I have so far:(attachment)

Answer 2

for the full question: 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 3

well, you have P = 2(l+w), using some calculus we can determine that the rate of change of the perimeter is P' = 2l' + 2w'

since you have w determine in terms of l. then w' = -4/l^2, and l'=1

P' = 2 + 2(4)/l^2, this is smallest when P'=0

0 = 2 + 2(4)/l^2

0 = 1 + 4/l^2

but this is only 0 when l^2 = -2 which isnt possible in real values.

Answer 4

but thats just my attempt at it :)

Answer 5

I think you may have forgotten the negative on -4/l^2 when you were plugging it into the equation, if so wouldn't it be l^2=2

Answer 6

... you are correct lol

Answer 7

it looks then like a square gives the smallest perimeter for the greatest area.

Answer 8

so technically 2 is my answer for the values of l and w?

Answer 9

yes

Answer 10

ok much obliged

Answer 11

good luck