1. The problem statement, all variables and given/known data Theorem: Let f: M->R where M is a open subset of Rn Suppose f is C2(M) Let x E M such that "gradient of f at x" = 0 and the Hessian of f at x is positive definite Then x is a strict local minimum point of f. The above theorem is given in my textbook. If instead we have "gradient of f at x" = 0 and the Hessian of f at x is positive SEMI-definite, can we conclue that x is a local minimum point of f? Why or why not? This puzzles me and I can't find this in the textbook. 2. Relevant equations Unconstrained optimziation 3. The attempt at a solution N/A Any help is appreciated!