3. Some pictures of visualization of a numerical method for determining the type of local extrema of functions with two variables on a contour map without using derivatives
Here are explanatory images from the [url=https://www.geogebra.org/m/v6pwykyh]applet[/url].
[size=85]Concentric closed contour lines always indicate either a local minimum or a local maximum. If a contour line intersects itself, the point could be a saddle point, local minimum, or local maximum. [/size]
1. ●Cross-shaped contour lines for both the saddle point, known as the monkey saddle, and the local minimum
2 and 3. ●Saddle points with "three" and "four" legs
[size=85]In the case of saddle point "four" legs at the point (0,0,0), the function f(x,y) as well as its derivatives have an uncertainty - subject of discussion![/size]
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[size=85]Mappings for the cases of three stationary points.[br] Localization of points on[br](a) contour map,[br](b) a graph of f(x,y),[br](c) a fragment, in a small domain.[br] For a detailed discussion of Example 7 on the scheme for calculating stationary points of a function of two variables, see the [url=https://mathinsight.org/local_extrema_examples_two_variables]link[/url].[/size][br]
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[size=85]Displaying images of the function f(x,y) and its fragment.[/size]
f(x,y)=x y (x+y)(1+y)
