Uncover Critical Points with Ease

Enter your multivariable function and variables to instantly find critical points. Visualize and understand calculus concepts interactively.

Function Details

Function (e.g., x^3 - 3*x*y + y^3):

f(x, y, ...) =

Variables (e.g., x, y):

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.