Juanita wishes to have a rectangular garden in her backyard with an area of 60 ft2.

Question

Juanita wishes to have a rectangular garden in her backyard with an area of 60 ft².

Letting x denote the width of the garden, find a function f in the variable x giving the length of the fencing required to construct the garden.

f(x) = 

 

What is the domain of this function? (Enter your answer using interval notation.)

Answer 1

Area = A =xy=60 x=width, y=length

y = f(x) =60/x

domain is 0 < x < infinity

interval notation: (0, infinity)

Perimeter = P(x) = 2(x+y)= 2(x+60/x) = 2x +120/x= length of fencing required

P(x) = 2x + 120/x

P'(x) = 2-120/x^2=0

x^2 = 60

x = sqr60 = y = side that minimizes fencing required