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The divide and conquer algorithm for solving equations discussed
in the last chapter can be applied to finding extrema of functions
of one variable, or even of functions defined parametrically
on a curve. Suppose for example you seek a local maximum of F on a curve.
To get started you need to find three values of the parameter
used to define the curve, such that the value of F is greater
at the point on the curve defined by the middle parameter
value than it is at the other two points. Suppose these parameter
values are a b and c. You can then examine the function F
for parameter values Exercises:14.3 Devise a plan for carrying this method out for a specific problem. 14.4 Execute it on a spreadsheet. |
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The
maximum of the value of F at these two points and at b will
be the center of three parameter values with the same property
as a b and c, namely the value of F at the middle one greater
than its value at the others, but they will be closer together.
Iterating this step will close in on a solution.