SOLUTION: Calculus Optimization Question
A rectangular garden is to be surrounded by a low fence. There is only 100 feet of fencing available for all four sides. What is the largest pos
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A rectangular garden is to be surrounded by a low fence. There is only 100 feet of fencing available for all four sides. What is the largest pos
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Question 1142707: Calculus Optimization Question
A rectangular garden is to be surrounded by a low fence. There is only 100 feet of fencing available for all four sides. What is the largest possible area of the garden that can be fenced? Answer by ikleyn(52780) (Show Source):
If x is the length of the garden, then its width is feet, and the area is
A(x) = =
They want you find the maximum of the function A(x) using Calculus.
For it, differentiate A(x) over x and equate the derivative to zero:
A'(x) = -2x + 50 = 0,
which gives you x = = 25 feet.
Thus you obtain the
ANSWER. Under given conditions, the maximum area is achieved for the square of the side length equal to
one fourth of the given perimeter, i.e. 25 feet.
This result is VERY WELL known and can be obtained by means of Algebra, too.
