For the largest area, half the fence is used parallel to the river, and the other half is used for the two ends of the rectangular space.
The dimensions are 475 m by 237.5 m.
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Let x represent the length along the river. Then the area (A) is found as
.. A = x*(950 -x)/2
This equation describes a parabola with its vertex (maximum) halfway between the zeros of x=0 and x=950. That is, the maximum area is achieved when half the fence is used parallel to the river.
First you need to find the slope of the line:

m=6-(-2) / (-1)-0 =-8
equation of line is:
y=mx+b
y=-8x+6
for absolute value function:
if x<0
y=-8x+6
if x>0
y=+8x-6
Compute the necessary values/derivatives of
at
:






Taylor's theorem then says we can "approximate" (in quotes because the Taylor polynomial for a polynomial is another, exact polynomial)
at
by


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Another way of doing this would be to solve for the coefficients
in

by expanding the right hand side and matching up terms with the same power of
.
Slope is rise over run which is -4/15