Rectangle R has varying length l and width w but
with a constant perimeter of 4 feet.
a) Express the area A as a function of length l. Write a list of everything you know about this function.
b) For what values of l and w will the area of R be the greatest? Give an algebraic explanation. Then give a geometric explanation. Be sure to include a graph with relevant points labeled.

Question

Rectangle R has varying length l and width w but
with a constant perimeter of 4 feet.
a) Express the area A as a function of length l. Write a list of everything you know about this function.
b) For what values of l and w will the area of R be the greatest? Give an algebraic explanation. Then give a geometric explanation. Be sure to include a graph with relevant points labeled.

anonymous · Answer

I actually have the answer to part a already

anonymous · Answer

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.

anonymous · Answer

^^^^ part 2