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Derivatives and Graphing : Local Maxima and Minima and Sketching Graphs

The function has a derivative everywhere and has just one critical point, . In parts (a)-(d), you are given additional conditions. In each case decide whether is a local maximum, a local minimum, or neither. Explain your reasoning. Sketch possible graphs for all four cases.
a)

b)

c)

d)

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Local Maxima and Minima and Sketching Graphs are investigated using derivatives. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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