Fill in the blank with "all", "no", or "some" to make the following statements true. note that "some" means one or more instances, but not all.
if your answer is "all", then give a brief explanation as to why.
if your answer is "no", then give an example and a brief explanation as to why.
if your answer is "some", then give two specific examples that illustrate why your answer it not "all" or "no". be sure to explain your two examples.
an example must include either a graph or a specific function.
(a) for functions f, if f ′′(0) = 0, there is an inflection point at x = 0.
(b) for functions f, if f ′ (p) = 0, then f has a local minimum or maximum at x = p.
(c) for functions f, a local minimum of a function f occurs at a critical point of f.
(d) for functions f, if f ′ is continuous and f has no critical points, then f is everywhere increasing or everywhere decreasing.