Critical Points Calculator

A critical points calculator solves f'(x) = 0 for a polynomial and says what happens at each solution. Type a polynomial in x up to the eighth power and it returns the derivative, the second derivative, every real critical point with the value of f there, and the classification from the second derivative test, falling back to the sign of the first surviving derivative when that test is inconclusive. A second action takes a closed interval and reports the absolute maximum and minimum on it, listing every candidate. Only polynomials are accepted; anything with a root, a logarithm or a trigonometric term is refused rather than approximated.