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 Rbecause of this behavior? Could you have made a similar statement about Rback in Task 1?

c) For what values of land w will the perimeter of R be the least? Give a geometric explanation. Be sure to include a graph with relevant p

Answer 1

A = l*w =4
Perimeter, P = 2(l + w) w = 4/l substitute in expression for P
P = 2(l + 4/l) simplify
P = 2(l^2 + 4)/4 = (l^2 + 4)/2 = l^2/2 + 2
I see a function with the highest power of 2 a +ve coefficient of 1/2 and a shift of 2
a parabola

Answer 2

Is this the answer for section a?

Answer 3

most of it yes! need to find the domain
I think it touched on some of b as well
do the picture show the vertex etc
also asymptotic is that it never touches because must have both values L and w to get the area or perimeter

Answer 4

And how do I find the domain?
And for the vertex do I just plug in the equation to my graphing calculator?

Answer 5

Like how do I show the picture ?

Answer 6

do you know what a parabola looks like?
the vertex would be 2,4 or -2, 4 don't remember the shift left or right it is a bit steep, opens up

by all means use your calculator to be more specific

hope this helped