SOLUTION: Please help me with this problem.I don't understand it. My teacher never went over these kinds of problems in class. I would really appreciate it if you would explain and answer.

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Question 697679: Please help me with this problem.I don't understand it. My teacher never went over these kinds of problems in class. I would really appreciate it if you would explain and answer.
A farmer has 526 meters of fencing available to enclose a rectangular portion of his land. One side of the rectangle being fenced lies along a river, so only three sides require fencing.
(a) Express the area A of the rectangle as a function of x, where x is the length of the side parallel to the river.
(b) For what value of x is the area largest?
Thanks in advance!
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
is the length of the side parallel to the river.
Each of the sides that are perpendicular to the river
are
Let = area of enclosed portion

This is a parabola which has a maximum because the
coefficient of the term is negative and the
term is positive. The maximum is at
when the equation has the form

263 meters answer
This is the x-co-ordinate of the maximum area, which is the
length of fencing parallel to the river.
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If you want the maximum Area, just plug this back into the equation

m2
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It's easy to test this result. if is slightly more than or less
than , the area should go down slightly also
If I say , then

It went down
You can check for
The area should also go down by roughly
the same amount.