Question

A farmer will make a rectangular pen with 100 feet of fence using part of his barn for one side of the pen. What is the largest area he can enclose?

Answer 1

100/4=25*25=625

Answer 2

I know the answer, but i need the work. Answer is 1250

Answer 3

is that the actual answer?

Answer 4

The perimeter:
2(x + y) = 100 + x
The area:
x * y = area

2x + 2y = 100 + x
2y = 100 + x - 2x
y = 50 - 0.5x

x * (50 - 0.5x) = area
-0,5x^2 + 50x = area

First derivative:
-x + 50

Solve for x:
x = 50

So y must be:
2x + 2y = 100 + x
2 * 50 + 2 * y = 100 + 50
100 + 2y = 150
2y = 50
y = 25

Test drive:
x * y = 50 * 25 = 1250

Answer 5

The first derivative is used for finding maximum point(s).

Answer 6

Thanks :D