Optimisation problems type 2 (First derivative test): Find local maximum and minimum of y = f(x) using first derivative: SIG787 Mathematics for AI Assignment 1 2025 Tri 1 Page 7 of 9 Find all critical points of f(x). If for a critical point x = c, f changes from positive to negative (f changes from increasing to decreasing), x = c is a local maximum point. If for a critical point x = c, f changes from negative to positive (f changes from decreasing to increasing), x = c is a local minimum point. Optimisation problems type 2 (Second derivative test): Find local maximum and minimum of y = f(x) using second derivative: Find all critical points of f(x). For a critical point x = c, if f(c) = 0 and f(c) > 0, x = c is a local minimum. For a critical point x = c, if f(c) = 0 and f(c) < 0, x = c is a local maximum. if f(c) = 0, the test is inconclusive. It does not give any useful information, and we need to use other techniques to decide the type of stationary point