๐Critical Points & Extrema Calculator
Enter a polynomial to find its critical points and classify each as a local max, local min, or neither.
Use ^ for powers, terms separated by + or โ. Example: 2x^4 - 8x^2 + 3
Free Critical Points Calculator
This critical points calculator finds where a polynomial's derivative equals zero, then applies the first derivative test โ checking the sign of f'(x) just before and after each point โ to classify it as a local maximum, local minimum, or neither.
Critical points are where a function's slope is momentarily flat, which is exactly where local extrema occur (along with possible inflection points where the slope doesn't change sign). This tool differentiates your polynomial symbolically, solves for its real roots, and evaluates the sign change around each one.
Supports any polynomial degree. Free, runs entirely in your browser, no sign-up required.