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Fill in the blank with “all”, “no”, or “some” to make the following statements true. Note...

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Advance Math

Fill in the blank with “all”, “no”, 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.

Answer & Explanation Solved by verified expert
4.0 Ratings (653 Votes)
a For SOME functions if there is an inflection point at First consider the function We know that is an inflection point for Therefore the answer cannot be NOIf we consider then and But is not an inflection point since is concave upward in all its domainb For    See Answer
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