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.