About the Critical Points & Extrema Calculator
A free tool for finding and classifying the critical points of a polynomial.
What it is
This calculator differentiates a polynomial you enter, solves for the x-values where the derivative equals zero, and classifies each one as a local maximum, local minimum, or neither using the first derivative test โ checking the sign of f'(x) just before and after each point.
Features
Any polynomial degree
Works for quadratics, cubics, quartics, and beyond.
Automatic classification
Each critical point is labeled max, min, or neither.
Derivative shown
See f'(x) and how the roots were found.
Instant, private
Runs entirely in your browser. No data is sent anywhere.