# Section 3.4 Concavity and the Second Derivative Test

Education

26

All Questions

26

Multiple Choice

0

True False

0

Essay

0

Short Answer

0

Not Answered

Q 1

Determine the open intervals on which the graph of is concave downward or concave upward.
A)concave upward on
B)concave downward on ;concave upward on
C)concave downward on ;concave upward on
D)concave downward on
E)concave upward on ;concave downward on

Free

Multiple Choice

D

Q 2

Determine the open intervals on which the graph of is concave downward or concave upward.
A)concave downward on
B)concave upward on ;concave downward on
C)concave upward on ;concave downward on
D)concave downward on ;concave upward on
E)concave downward on ;concave upward on

Free

Multiple Choice

C

Q 3

Determine the open intervals on which the graph of the function is concave upward or concave downward.
A)concave upward: ;concave downward:
B)concave upward: ;concave downward:
C)concave upward: ;concave downward:
D)concave upward: ;concave downward:
E)concave upward: ;concave downward:

Free

Multiple Choice

B

Q 4

Determine the open intervals on which the graph of the function is concave upward or concave downward.
A)concave upward: ;concave downward:
B)concave upward: ;concave downward:
C)concave upward: ;concave downward:
D)concave upward: ;concave downward:
E)concave upward: ;concave downward:

Multiple Choice

Q 5

Determine the open intervals on which the graph of is concave downward or concave upward.
A)concave downward on ;concave upward on
B)concave downward on ;concave upward on
C)concave upward on ;concave downward on
D)concave downward on ;concave upward on
E)concave upward on ;concave downward on

Multiple Choice

Q 6

Find all points of inflection on the graph of the function .
A)
B)
C)
D)
E)

Multiple Choice

Q 7

Find the points of inflection and discuss the concavity of the function.
A)inflection point at ;concave upward on
;concave downward on
B)inflection point at ;concave downward on
;concave upward on
C)inflection point at ;concave downward on
;concave upward on
D)inflection point at ;concave downward on
;concave upward on
E)inflection point at ;concave upward on
;concave downward on

Multiple Choice

Q 8

Find the points of inflection and discuss the concavity of the function .
A)no inflection points;concave up on
B)no inflection points;concave down on
C)inflection point at ;concave up on
D)inflection point at ;concave up on
;concave down on
E)inflection point at ;concave down on

Multiple Choice

Q 9

Find all points of inflection,if any exist,of the graph of the function .Round your answers to two decimal places.
A)
B)
C)
D)
E)no points of inflection

Multiple Choice

Q 10

Find the point of inflection of the graph of the function on the interval .
A)
B)
C)
D)
E)

Multiple Choice

Q 11

Find the points of inflection and discuss the concavity of the function on the interval .
A)no inflection points.concave up on
B)concave downward on ;concave upward on
;inflection point at
C)no inflection points.concave down on
D)concave upward on ;concave downward on
;inflection point at
E)none of the above

Multiple Choice

Q 12

Find all points of inflection of the graph of the function on the interval .Round your answer to three decimal places wherever applicable.
A)
B)
C)
D)
E)

Multiple Choice

Q 13

Find the points of inflection and discuss the concavity of the function on the interval .
A)concave down on ;no points of inflection
B)concave upward on ;concave downward on
;inflection points at
and
C)concave downward on ;concave upward on
;inflection points at
and
D)concave up on ;no points of inflection
E)none of the above

Multiple Choice

Q 14

Find all points of inflection on the graph of the function .
A)
B)
C)
D)
E)

Multiple Choice

Q 15

Find all relative extrema of the function .Use the Second Derivative Test where applicable.
A)relative max: ;no relative min
B)no relative max;no relative min
C)relative max: ;relative min:
D)relative max: ;no relative min
E)relative min: ;relative max:

Multiple Choice

Q 16

Find all relative extrema of the function .Use the Second Derivative Test where applicable.
A)relative max: ;no relative min
B)relative min: ;no relative max
C)relative min: ;no relative max
D)relative max: ;no relative min
E)no relative max or min

Multiple Choice

Q 17

Find all relative extrema of the function .Use the Second Derivative Test where applicable.
A)relative minimum:
B)relative minimum:
C)relative maximum:
D)relative minimum:
E)relative maximum:

Multiple Choice

Q 18

Find all relative extrema of the function .Use the Second Derivative Test where applicable.
A)relative max: ;no relative min
B)no relative max or min
C)relative min: ;no relative max
D)relative max: ;relative min:
E)relative max: ;no relative min

Multiple Choice

Q 19

Locate any relative extrema and inflection points of the function .Use a graphing utility to confirm your results.
A)relative minimum value: ;no inflection points
B)relative minimum value: inflection point:
C)relative maximum value: inflection point:
D)relative minimum value: no inflection points
E)relative maximum value: ;no inflection points

Multiple Choice

Q 20

Determine the x-coordinate(s)of any relative extrema and inflection points of the function .
A)relative minimum: ;inflection point:
B)no relative extrema;inflection point:
C)relative minimum: ;no inflection points
D)no relative extrema;inflection point:
E)relative maximum: inflection point:

Multiple Choice

Q 21

Determine the x-coordinate(s)of any relative extrema and inflection points of the function .
A)relative minimum: ;no inflection points
B)relative maximum: ;inflection point:
C)no relative maximum or minimum;inflection point:
D)no relative extrema or inflection points.
E)relative minimum: ;inflection point:

Multiple Choice

Q 22

The graph of f is shown.Graph f,f' and f'' on the same set of coordinate axes.
A)
B)
C)
D)
E)none of the above

Multiple Choice

Q 23

The graph of f is shown.Graph f,f' and f'' on the same set of coordinate axes.
A)
B)
C)
D)
E)none of the above

Multiple Choice

Q 24

Find the cubic function of the form where and the coefficients are real numbers,which satisfies the conditions given below.
Relative maximum: Relative minimum: Inflection point:
A)
B)
C)
D)
E)

Multiple Choice

Q 25

Suppose the deflection D of a beam of length L is ,where x is the distance from one end of the beam.Find the value of x that yields the maximum deflection.
A)
B)
C)
D)
E)

Multiple Choice

Q 26

Suppose a manufacturer has determined that the total cost C of operating a factory is where x is the number of units produced.At what level of production will the average cost per unit be minimized? (The average cost per unit is . )
A) units
B) units
C) units
D) units
E) units

Multiple Choice