First and second derivative tests
Differentiation · Mathematics
Study notes
Q: Classify the critical points of f(x) = x^3 - 3x using both tests. f'(x) = 3x^2-3 = 0 at x = ±1. First test: at x=-1, f' changes + to -: local max. At x=1, - to +: local min. Second test: f''(x) = 6x. f''(-1) = -6 < 0: max. f''(1) = 6 > 0: min. Agree!