What is the solution to the system of linear equations graphed below?
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N.b., this is copied from an answer I wrote for someone else.
Thinking about the graph of y, the rate of change is zero whenever there is an extremum.
First, differentiate y.
Next, find the zeros of y' by factoring.
Now, we substitute these x-values into the original equation to find the coordinates.
Thinking about the graph of y, the rate of change is zero whenever there is an extremum.
First, differentiate y.
Next, find the zeros of y' by factoring.
Now, we substitute these x-values into the original equation to find the coordinates.
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.
_____
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.
The dimensions are 475 m by 237.5 m.
_____
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.