**1.** _{The second derivative of the function is given by } _{. At what values of in}
the interval does the graph of have a point of inflection?

**A** 2.229 only

**B** 0 and 2.229

**C** and 0.987

**D** , 0, and 1.603

**2.** _{The second derivative of the function is given by } _{. The function has}
many critical points, two of which are at and . Which of the following statements is
true?

**A** has a local minimum at and at .

**B** has a local minimum at and a local maximum at .

**C** has a local maximum at and a local minimum at .

**D** has a local maximum at and at .

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**A** 1

**B** 2

**C** 6

**D** 26

**4.** Let be the function defined by . What is the absolute minimum value of on
the interval ?

**A**

**B**

**C**

**D** 0

**A** 1

**B**

**C**

**D**

**6.**

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**A** and

**B** and

**C**

**D**

**7.**

**A** and

**B** and

**C** and

**D**

**8.** The Second Derivative Test cannot be used to conclude that is the location of a relative
minimum or relative maximum for which of the following functions?

**A** , where

**B** , where

**C** , where

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The graph of , the second derivative of the continuous function , is shown above on the interval . On this interval has only one critical point, which occurs at . Which of the following statements is true about the function on the interval ?

**A** has a relative minimum at but not an absolute minimum.

**B** The absolute minimum of is at .

**C** has a relative maximum at but not an absolute maximum.

The graph of , the derivative of the continuous function , is shown above on the interval . The graph of has horizontal tangent lines at , , , and , and a vertical tangent line at . On which of the following intervals is the graph of both decreasing and concave up ?

**A** and

**B** and only

**C** and only

**D** , , and only

**11.**

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**A** The function has a relative maximum at .

**B** The graph of has a point of inflection at .

**C** The function has a relative minimum at .

**D** The graph of has a point of inflection at .

**12.**

The graph of , the derivative of the continuous function , is shown above on the interval . Which of the following statements is true about on the interval ?

**A** has two relative extrema, and the graph of has three points of inflection.

**B** has three relative extrema, and the graph of has three points of inflection.

**C** has three relative extrema, and the graph of has four points of inflection.