First and Second Derivative Tests Quiz



Sections 4.1-4.3 Name:

1. Using analytic methods, find the intervals over which the function is increasing, decreasing, concave up and concave down. Find all extrema and state them properly. Find all the points of inflection and state them as ordered pairs. Finally sketch the function. Label points of inflection and all extrema. All answers must be justified to receive full credit.

[pic]

Find the absolute extrema of the function on the given interval.

2. [pic]

Show the following function satisfies the hypotheses of the Mean Value Theorem and find the value, c, that satisfies [pic].

3.[pic]

4. By referring to the graph of f(x), fill in the table with positive, negative, zero, or DNE.

|x |f ′(x) |

|-1 | |

|0 | |

|2 | |

|4 | |

|5 | |

|6 | |

|7 | |

|8 | |

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