### For a continuous function f,
(1) if f' changes sign from positive to negative at a critical point c, then f has a local maximum value at c;
(2) if f' changes sign from negative to positive at a critical point c, then f has a local minimum value at c
(3) if f' does not change sign at a critical point c, then f has no local extreme value at c;
(4) if f'<0 (f'>0) for x>a where a is a left endpoint in the domain of f, then f has a local maximum (minimum) value at a;(5) if f'<0 (f'>0) for x<b where b is the right endpoint in the domain of f, then f has a local minimum (maximum) value at b