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Topic: Help.
Replies: 4   Last Post: Jan 17, 2006 2:08 PM

 Messages: [ Previous | Next ]
 ticbol Posts: 116 Registered: 1/25/05
Re: Help.
Posted: Jan 17, 2006 3:34 AM

r9ronaldo wrote:
> A farmer's land is borded on one side by a straight river. Find the dimensions of the largest plot that can be enclosed on three sides by a fence of length P, the fourth side being the river.

-----------------
The plot is assumed to be rectangular.
Let x = side perpendicular to the river, so (P -2x) is the side
parallel to the river.
Area, A = x(P -2x)
A = Px -2x^2
Differentiate both sides with respect to x,
dA/dx = P -4x
For maximum, or minimum, A, set dA/dx to zero,
0 = P -4x
4x = P
x = P/4 -------for max or min A.

The second derivative of A with respect to x is d/dx of (P -4x), which
is (-4).
Negative, so x = P/4 is for max A.

Therefore, the largest plot is P/4 by P/2. ---------answer.

Date Subject Author
1/16/06 r9ronaldo
1/16/06 Paul Sperry
1/17/06 Don Taylor
1/17/06 ticbol
1/17/06 Jasen Betts