Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Compute the stationary points of a function of one or more variables
ResourceFunction["StationaryPoints"][expr, {var_{1},var_{2}, …}] computes the stationary points of expr with respect to the variables var_{i}. 

ResourceFunction["StationaryPoints"][{expr,domain},{var_{1},var_{2},…}] computes the stationary points of expr that lie within the specified domain. 

ResourceFunction["StationaryPoints"][…, "type"] limits the stationary points returned to those of the given type. 
ResourceFunction["StationaryPoints"][{expr,domain},…]
, the argument domain should be a boolean expression, typically an equality, inequality or logical combination thereof, involving the var_{i}.Find the stationary points of a function of one variable:
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Plot the function and its stationary points found above:
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Find the stationary points of a periodic function:
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Find the stationary points of a function over a restricted domain
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Find stationary points of a function of two variables:
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Find stationary points of a function of three variables when restricting to a plane:
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Using the Type option will return only stationary points of the given type:
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Using Automatic as the second argument gives an association of all stationary points:
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StationaryPoints will sometimes return results in terms of Root objects:
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Results such as these can be numericized by applying N:
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For functions with a repeating pattern of stationary points, StationaryPoints returns results in terms of one or more undetermined constants, which can take any integer value:
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For functions possessing one or more families of nonisolated stationary points, StationaryPoints may return only the isolated stationary points. For example, the function sin(x^{3}y^{3}) has lines of stationary points along both the x– and y– axes, as can be seen in the following plot:
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These, however, are excluded from the results of StationaryPoints:
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