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A serpentine curve is a curve whose equation is of the form
Equivalently, it has a parametric representation
or functional representation
The curve has an inflection point at the origin. It has local extrema at x = ± a {\displaystyle x=\pm a} , with a maximum value of y = b / 2 {\displaystyle y=b/2} and a minimum value of y = − b / 2 {\displaystyle y=-b/2}.
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