Local Extrema Classifier: Find Minima, Maxima & Saddle Points
Easily classify critical points of multivariable functions as local minima, local maxima, or saddle points. Input your function and critical points to analyze using our online tool.
Function Details
Enter the function in terms of x and y. Use '^' for power, '*' for multiplication.
Enter critical points as a JSON array of coordinate pairs.
Enter the variables separated by commas.
Classification Results
Hessian Matrices
| Point | Hessian Matrix | Classification |
|---|---|---|
About Local Extrema Classifier
The Local Extrema Classifier tool helps you identify critical points of a function of two variables. In calculus, finding local minima, maxima, and saddle points is crucial for understanding the behavior of functions. This tool uses the Hessian matrix and the determinant test to classify these points.
- Local Minimum: A point where the function value is less than or equal to the values at all nearby points.
- Local Maximum: A point where the function value is greater than or equal to the values at all nearby points.
- Saddle Point: A critical point that is neither a local minimum nor a local maximum.
- Hessian Matrix: A square matrix of second-order partial derivatives of a scalar-valued function.
- Determinant Test: Uses the determinant and trace of the Hessian matrix to classify critical points.
To use the tool, input your function, critical points, and variables. The tool will calculate the Hessian matrix for each point and classify them accordingly.