.
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.
See the lessons
- HOW TO complete the square to find the minimum/maximum of a quadratic function
- Briefly on finding the minimum/maximum of a quadratic function
- HOW TO complete the square to find the vertex of a parabola
- Briefly on finding the vertex of a parabola
- A rectangle with a given perimeter which has the maximal area is a square
- A farmer planning to fence a rectangular garden to enclose the maximal area
in this site.