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.
