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.

Ready to use it?

Free, no sign-up required.

Open the Critical Points & Extrema Calculator