[size=85]f₄(x, y) = k[sub]f[/sub]*(x⁴ + y⁴ - 8x² - 18y² - 2)[br]*[i]The applet will work at a much faster speed if you download it to a desktop computer.[br][i] The order of operations for computing stationary points can be found in the [i][url=https://www.geogebra.org/m/te2vqwjq]applet[/url].[/i][/i][br][br] [b]Interactively find and compute local extrema of a nonlinear function of two variables without using its derivatives.[/b][br] Under the applet, you will find the stationary points of the function in question, calculated on a desktop computer, and you can compare them with more accurate calculations in CAS based on knowledge of the analytical formulas for its partial derivatives.[br] [/i]The iteration process consists of no+2 steps. When searching for local [b][color=#ff0000]maxima[/color][/b] and [b][color=#0000ff]minima[/color][/b], the function values ​​of the iteration points are sorted for all steps. However, such sorting is difficult because these values ​​coincide within the accuracy of the GeoGebra algebra. Therefore, to find the [b][color=#ff0000]largest[/color]/[color=#0000ff]smallest[/color][/b] value, this sorting is additionally performed in GeoGebra CAS with higher accuracy.[br] To calculate [b][color=#93c47d]saddle[/color][/b] points,[b] d[/b][sub][b]i[/b] [/sub]- the distance between two characteristic points for each iteration - was [i]chosen as a criterion[/i]. The iteration is considered optimal if this distance is [i]minimal[/i]. These distances for different iterations differ enough that the calculations can be done without using CAS.[br] *Explanations of the algorithms for searching for stationary points can be found in the applets [url=https://www.geogebra.org/m/ef6s3hyj]1[/url] and [url=https://www.geogebra.org/material/show/id/hcgdjdyf]2[/url].[/size]