Frequently Asked Questions

A critical point of f(x) is a value of x where f'(x) = 0 (or is undefined). For polynomials, that means every x-value where the derivative equals zero.

The first derivative test classifies a critical point by checking the sign of f'(x) just before and after it: positive-to-negative means a local maximum, negative-to-positive means a local minimum, and no sign change means neither.

No. Some critical points are saddle points or inflection points where the slope touches zero but doesn't change sign, so the function keeps increasing or decreasing through that point.

It symbolically differentiates your polynomial term by term, then numerically solves f'(x) = 0 by scanning for sign changes and refining each root with bisection.

Standard polynomial notation using ^ for exponents, such as x^3 - 3x^2 - 9x + 5. Terms can be separated by + or −.

Linear functions (degree 1) have a constant, non-zero derivative, so they have no critical points and no local extrema — the calculator will tell you this.

Yes, the numerical root-finding approach works for polynomials of any degree, not just quadratics and cubics that have closed-form solutions.

A critical point is where the first derivative is zero; an inflection point is where the second derivative changes sign (concavity flips). They can occur at different x-values.

It finds local extrema. For polynomials with even degree and a positive/negative leading coefficient, the global extremum is typically the most extreme local one, but you should check end behavior for unbounded domains.

Yes, completely free with no sign-up, and it runs entirely in your browser.