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Critical Points Analyzer

Analyze functions of two variables to find and classify critical points as local maxima, minima, or saddle points

Function Input

f(x,y) =          

Supported operations

Basic operations:
+-*/^()
Trigonometric:
sin(x)cos(y)tan()sec()csc()cot()
Exponential & Logarithmic:
exp(x)log(x)log10(x)sqrt(x)
Other functions:
abs(x)floor(x)ceil(x)
Examples:
x^2 + y^2
sin(x) * cos(y)
exp(-(x^2 + y^2))

Example Functions

1x2+y2x^2 + y^2
2x2−y2x^2 - y^2
3sin⁡x⋅cos⁡y\sin{x} \cdot \cos{y}
4exp⁡−(x2+y2)\exp{-(x^2 + y^2)}
5x3−3x⋅y2x^3 - 3x \cdot y^2
6x4+y4−x2−y2x^4 + y^4 - x^2 - y^2
7log⁡(x2+y2+1)\log{(x^2 + y^2 + 1)}
8x2⋅exp⁡(−x2−y2)x^2 \cdot \exp{(-x^2-y^2)}
9sin⁡(x2+y2)\sin{(x^2 + y^2)}
10x2y−y3x^2y - y^3

Enter a function to analyze

Input a function of two variables (x and y) in the panel on the left and click "Analyze Function" to see critical points and visualizations.