Uncover Critical Points with Ease
Enter your multivariable function and variables to instantly find critical points. Visualize and understand calculus concepts interactively.
Function Details
Critical Points
Understanding Critical Points
In multivariable calculus, critical points are essential for finding local maxima, minima, and saddle points of a function. A critical point occurs where the gradient of the function is zero or undefined. For a function f(x, y), this means solving the system of equations ∂f/∂x = 0 and ∂f/∂y = 0.
How to use this tool:
- Enter your multivariable function in the 'Function' input field. Use variables like x, y, z, etc., and standard math notation (e.g.,
x^2 + y^2,sin(x)*cos(y)). - Specify the variables in the 'Variables' input field, separated by commas (e.g.,
x, y). - Click the 'Calculate Critical Points' button to find the critical points.
- The critical points will be displayed in JSON format below. You can copy them for further analysis.
This tool uses mathjs library for mathematical computations.
You may also like these tools
Local Extrema Classifier: Find Minima, Maxima & Saddle Points
Easily classify critical points of multivariable functions as local minima, local maxima, or saddle points.
Jacobian Matrix Calculator
Easily compute the Jacobian matrix of a multivariable function online.
Hessian Matrix Calculator
Compute the Hessian matrix of a multivariable function, inspect every second-order partial derivative, and study local curvature with a compact matrix-first workflow.