SOLUTION: Suppose you have 80 feet of fence to enclose a rectangular garden. the Function A=40x-x^2 gives you the area of the garden in the square feet where x is the width in feet. A. Wh

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Suppose you have 80 feet of fence to enclose a rectangular garden. the Function A=40x-x^2 gives you the area of the garden in the square feet where x is the width in feet. A. Wh      Log On


   

Question 1021476: Suppose you have 80 feet of fence to enclose a rectangular garden. the Function A=40x-x^2 gives you the area of the garden in the square feet where x is the width in feet.
A. What is the maximum area?
B. What width will yield the maximum area?
Found 2 solutions by Fombitz, rothauserc:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

It's a quadratic, convert to vertex form.
A%28x%29=40x-x%5E2
A%28x%29=-x%5E2%2B40x
A%28x%29=-%28x%5E2-40x%29
A%28x%29=-%28x%5E2-40x%2B400%29%2B400
A%28x%29=-%28x-20%29%5E2%2B400
So the maximum occurs when x=20ft and the value is A%2820%29=400ft%5E2

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
A = 40x - x^2 (note that this is a parabola that curves downward)
:
take the first derivative of A
:
A' = 40 - 2x
:
now set A' = 0 and solve for x
:
40 - 2x = 0
:
2x = 40
:
x = 20
:
A) x = 20 means the width is 20 feet
A = 40(20) - 20^2 = 400
maximum area is 400 square feet
:
B) width of 20 feet yields max area