Suppose f'(x) is continuous over an interval ? ? x ? b, and a

Suppose f'@) is continuous over an interval a '.c b, and a < c < d < b. If f' (c) 5, then (check all that apply) f(c) is decreasing through a; = c f(c) 5 f(c) exists f does not have a minimum at c = c f does not have a maximum at c = c f(c) is increasing through c c If f' (d) 5, then (check all that apply) f(d) exists f does not have a maximum at = d f does not have a minimum at d f(d) = 5 f(:c) is increasing through = d f(c) is decreasing through a: d Based on this, we know that for some a; between a,' c and d: f has a maximum f has a minimum f does not exist