Fill in the blank with “allâ€, “noâ€, or “some†to make thefollowing statements true. Note that “some†means one or moreinstances, but not all. • If your answer is “all,†then give abrief explanation as to why. • If your answer is “no,†then give anexample and a brief explanation as to why. • If your answer is“some,†then give two specific examples that illustrate why youranswer 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 pointat x = 0. (
b) For functions f, if f′(p) = 0, then f has a local minimum ormaximum at x = p.
(c) For functions f, a local minimum of a function f occurs at acritical point of f.
(d) For functions f, if f′ is continuous and f has no criticalpoints, then f is everywhere increasing or everywheredecreasing.
