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Unit 5 Progress Check: MCQ Part B

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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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Copyright © 2017. The College Board. These materials are part of a College Board program. Use or distribution of these materials online or

in print beyond your school’s participation in the program is prohibited. Page 2 of 8

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

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A 1

B

C

D

6.

(4)

Copyright © 2017. The College Board. These materials are part of a College Board program. Use or distribution of these materials online or

in print beyond your school’s participation in the program is prohibited. Page 4 of 8

A and

B and

C

D

7.

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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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Copyright © 2017. The College Board. These materials are part of a College Board program. Use or distribution of these materials online or

in print beyond your school’s participation in the program is prohibited. Page 6 of 8

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.

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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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Copyright © 2017. The College Board. These materials are part of a College Board program. Use or distribution of these materials online or in print beyond

your school’s participation in the program is prohibited. Page 8 of 8

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.

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