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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.



