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Deck 4: Section 4: Applications of Differentiation
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Question
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
; concare 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 
A) inflection point at
; concave upward on ; concave downward on B) inflection point at
; concare 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 
Question
Find all points of inflection on the graph of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
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
. Round your answers to two decimal places.A)
B)
C)
D)
E) no points of inflection
Question
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
. Use a graphing utility to confirm your results.A) relative minimum value:
; no inflection pointsB) relative minimum value:
inflection point: C) relative maximum value:
inflection point: D) relative minimum value:
no inflection pointsE) relative maximum value:
; no inflection points Question
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)
on the interval . Round your answer to three decimal places wherever applicable.A)
B)
C)
D)
E)
Question
Find the points of inflection and discuss the concavity of the function 
on the interval 
.
A) no inflection points. concave up on
B) concave upward on
; concave downward on 
; inflection point at 
C) no inflection points. concave down on
D) concave downward on
; concave upward on 
; inflection point at 
E) none of the above
on the interval .A) no inflection points. concave up on
B) concave upward on
; concave downward on ; inflection point at C) no inflection points. concave down on
D) concave downward on
; concave upward on ; inflection point at E) none of the above
Question
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:
. Use the Second Derivative Test where applicable.A) relative minimum:
B) relative minimum:
C) relative maximum:
D) relative minimum:
E) relative maximum:
Question
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: 
.A) relative minimum:
; inflection point: B) no relative extrema; inflection point:
C) relative minimum:
; no inflection pointsD) no relative extrema; inflection point:
E) relative maximum:
inflection point: Question
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 upward on
E) concave downward on
; concave upward on 
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 upward on
E) concave downward on
; concave upward on Question
Find all points of inflection on the graph of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
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 downward on
; concave upward on 
; inflection points at 
and 
C) concave upward on
; concave downward on 
; inflection points at 
and 
D) concave up on
; no points of inflection
E) none of the above
on the interval .A) concave down on
; no points of inflectionB) concave downward on
; concave upward on ; inflection points at and C) concave upward on
; concave downward on ; inflection points at and D) concave up on
; no points of inflectionE) none of the above
Question
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: 
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: Question
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 min:
; relative max: 
D) relative min:
; no relative max
E) relative min:
; relative max: 
. Use the Second Derivative Test where applicable.A) relative max:
; no relative minB) no relative max; no relative min
C) relative min:
; relative max: D) relative min:
; no relative maxE) relative min:
; relative max: Question
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
. Use the Second Derivative Test where applicable.A) relative max:
; no relative minB) relative min:
; no relative maxC) relative min:
; no relative maxD) relative max:
; no relative minE) no relative max or min
Question
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 x = 16; concave up on
D) inflection point at x = 0; concave up on
; concave down on 
E) inflection point at x = 16; concave down on
.A) no inflection points; concave up on
B) no inflection points; concave down on
C) inflection point at x = 16; concave up on
D) inflection point at x = 0; concave up on
; concave down on E) inflection point at x = 16; concave down on
Question
Find all relative extrema of the function 
. Use the Second Derivative Test where applicable.
A) relative max: (1, -2); no relative min
B) no relative max or min
C) relative min: (0, -3); no relative max
D) relative max: (1, -2); relative min: (0, -3)
E) relative max: (0, -3); no relative min
. Use the Second Derivative Test where applicable.A) relative max: (1, -2); no relative min
B) no relative max or min
C) relative min: (0, -3); no relative max
D) relative max: (1, -2); relative min: (0, -3)
E) relative max: (0, -3); no relative min
Question
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: 
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: Question
Find the point of inflection of the graph of the function 
on the interval 
.
A)
B)
C)
D)
E)
on the interval .A)
B)
C)
D)
E)
Question
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 
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 Question
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 
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 Question
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)
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)
Question
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
A)
B)
C)
D)
E) none of the above
Question
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 C/x.)
A)
B)
C)
D)
E)
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 C/x.)A)
B)
C)
D)
E)
Question
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)
where and the coefficients are real numbers, which satisfies the conditions given below. Relative maximum: Relative minimum: Inflection point: A)
B)
C)
D)
E)
Question
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
A)
B)
C)
D)
E) none of the above
Question
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: 
.A) relative minimum:
; no inflection pointsB) relative maximum:
; inflection point: C) no relative maximum or minimum; inflection point:
D) no relative extrema or inflection points.
E) relative minimum:
; inflection point: 
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Deck 4: Section 4: Applications of Differentiation
1
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 ; concare 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
A) inflection point at
; concave upward on ; concave downward on B) inflection point at
; concare 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 inflection point at ; concave upward on ; concave downward on
; concave upward on ; concave downward on 2
Find all points of inflection on the graph of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
3
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
. Round your answers to two decimal places.A)
B)
C)
D)
E) no points of inflection
no points of inflection
4
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
. Use a graphing utility to confirm your results.A) relative minimum value:
; no inflection pointsB) relative minimum value:
inflection point: C) relative maximum value:
inflection point: D) relative minimum value:
no inflection pointsE) relative maximum value:
; no inflection points Unlock Deck
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5
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)
on the interval . Round your answer to three decimal places wherever applicable.A)
B)
C)
D)
E)
Unlock Deck
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6
Find the points of inflection and discuss the concavity of the function on the interval .
A) no inflection points. concave up on
B) concave upward on ; concave downward on ; inflection point at
C) no inflection points. concave down on
D) concave downward on ; concave upward on ; inflection point at
E) none of the above
on the interval .A) no inflection points. concave up on
B) concave upward on
; concave downward on ; inflection point at C) no inflection points. concave down on
D) concave downward on
; concave upward on ; inflection point at E) none of the above
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7
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:
. Use the Second Derivative Test where applicable.A) relative minimum:
B) relative minimum:
C) relative maximum:
D) relative minimum:
E) relative maximum:
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8
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:
.A) relative minimum:
; inflection point: B) no relative extrema; inflection point:
C) relative minimum:
; no inflection pointsD) no relative extrema; inflection point:
E) relative maximum:
inflection point: Unlock Deck
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9
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 upward on
E) concave downward on ; concave upward on
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 upward on
E) concave downward on
; concave upward on Unlock Deck
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10
Find all points of inflection on the graph of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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11
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 downward on ; concave upward on ; inflection points at and
C) concave upward on ; concave downward on ; inflection points at and
D) concave up on ; no points of inflection
E) none of the above
on the interval .A) concave down on
; no points of inflectionB) concave downward on
; concave upward on ; inflection points at and C) concave upward on
; concave downward on ; inflection points at and D) concave up on
; no points of inflectionE) none of the above
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12
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:
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: Unlock Deck
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13
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 min: ; relative max:
D) relative min: ; no relative max
E) relative min: ; relative max:
. Use the Second Derivative Test where applicable.A) relative max:
; no relative minB) no relative max; no relative min
C) relative min:
; relative max: D) relative min:
; no relative maxE) relative min:
; relative max: Unlock Deck
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14
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
. Use the Second Derivative Test where applicable.A) relative max:
; no relative minB) relative min:
; no relative maxC) relative min:
; no relative maxD) relative max:
; no relative minE) no relative max or min
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15
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 x = 16; concave up on
D) inflection point at x = 0; concave up on ; concave down on
E) inflection point at x = 16; concave down on
.A) no inflection points; concave up on
B) no inflection points; concave down on
C) inflection point at x = 16; concave up on
D) inflection point at x = 0; concave up on
; concave down on E) inflection point at x = 16; concave down on
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16
Find all relative extrema of the function . Use the Second Derivative Test where applicable.
A) relative max: (1, -2); no relative min
B) no relative max or min
C) relative min: (0, -3); no relative max
D) relative max: (1, -2); relative min: (0, -3)
E) relative max: (0, -3); no relative min
. Use the Second Derivative Test where applicable.A) relative max: (1, -2); no relative min
B) no relative max or min
C) relative min: (0, -3); no relative max
D) relative max: (1, -2); relative min: (0, -3)
E) relative max: (0, -3); no relative min
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17
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:
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: Unlock Deck
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18
Find the point of inflection of the graph of the function on the interval .
A)
B)
C)
D)
E)
on the interval .A)
B)
C)
D)
E)
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19
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
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 Unlock Deck
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20
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
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 Unlock Deck
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21
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)
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)
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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
A)
B)
C)
D)
E) none of the above
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23
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 C/x.)
A)
B)
C)
D)
E)
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 C/x.)A)
B)
C)
D)
E)
Unlock Deck
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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)
where and the coefficients are real numbers, which satisfies the conditions given below. Relative maximum: Relative minimum: Inflection point: A)
B)
C)
D)
E)
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25
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
A)
B)
C)
D)
E) none of the above
Unlock Deck
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26
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:
.A) relative minimum:
; no inflection pointsB) relative maximum:
; inflection point: C) no relative maximum or minimum; inflection point:
D) no relative extrema or inflection points.
E) relative minimum:
; inflection point: Unlock Deck
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