تكلم مع الذكاء الاصطناعي
Deck 4: Section 1 : Applications of Differentiation
ملء الشاشة (f)
سؤال
Sketch the graph of the function 
and locate the absolute extrema of the function on the interval 
.
A) left endpoint:
absolute minimum
Right endpoint:
absolute maximum
B) left endpoint:
absolute minimum
Right endpoint:
absolute maximum
C) left endpoint:
absolute minimum
Right endpoint:
absolute maximum
D) left endpoint:
absolute minimum
Right endpoint:
absolute maximum
E) left endpoint:
absolute minimum
Right endpoint:
absolute maximum
and locate the absolute extrema of the function on the interval .A) left endpoint:
absolute minimumRight endpoint:
absolute maximumB) left endpoint:
absolute minimumRight endpoint:
absolute maximumC) left endpoint:
absolute minimumRight endpoint:
absolute maximumD) left endpoint:
absolute minimumRight endpoint:
absolute maximumE) left endpoint:
absolute minimumRight endpoint:
absolute maximum
سؤال
Locate the absolute extrema of the function 
on the closed interval 
. Round your answers to four decimal places.
A) left endpoint:
Right endpoint:
absolute maximum
Critical points:
absolute minimum
B) left endpoint:
absolute minimum
Right endpoint:
absolute maximum
Critical points: none
C) left endpoint:
absolute minimum
Right endpoint:
absolute maximum
Critical points:
D) left endpoint:
absolute minimum
Right endpoint:
absolute maximum
Critical points: none
E) left endpoint:
Right endpoint:
absolute maximum
Critical points:
absolute minimum
on the closed interval . Round your answers to four decimal places.A) left endpoint:
Right endpoint:
absolute maximumCritical points:
absolute minimumB) left endpoint:
absolute minimumRight endpoint:
absolute maximumCritical points: none
C) left endpoint:
absolute minimumRight endpoint:
absolute maximumCritical points:
D) left endpoint:
absolute minimumRight endpoint:
absolute maximumCritical points: none
E) left endpoint:
Right endpoint:
absolute maximumCritical points:
absolute minimum سؤال
Locate the absolute extrema of the function 
on the closed interval 
.
A) absolute max:
; no absolute min
B) no absolute max or min
C) no absolute max; absolute min:
D) absolute max:
; absolute min: 
E) absolute max:
; absolute min: 
on the closed interval .A) absolute max:
; no absolute minB) no absolute max or min
C) no absolute max; absolute min:
D) absolute max:
; absolute min: E) absolute max:
; absolute min: سؤال
Find all critical numbers of of the function 
, 
.
A)
B)
C)
D)
E)
, .A)
B)
C)
D)
E)
سؤال
Locate the absolute extrema of the function 
on the closed interval 
.
A) absolute max:
; absolute min: 
B) no absolute max; absolute min:
C) absolute max:
; absolute min: 
D) absolute max:
; no absolute min
E) no absolute max or min
on the closed interval .A) absolute max:
; absolute min: B) no absolute max; absolute min:
C) absolute max:
; absolute min: D) absolute max:
; no absolute minE) no absolute max or min
سؤال
Locate the absolute extrema of the function 
on the closed interval 
.
A) The absolute
is 
, and it occurs at the left endpoint 
.
The absolute
is 
, and it occurs at the right endpoint 
.
B) The absolute
is 
, and it occurs at the right endpoint 
.
The absolute
is 
, and it occurs at the left endpoint 
.
C) The absolute
is 
, and it occurs at the left endpoint 
.
The absolute
is 
, and it occurs at the right endpoint 
.
D) The absolute
is 
, and it occurs at the right endpoint 
.
The absolute
is 
and it occurs at the left endpoint 
.
E) The absolute
is 
, and it occurs at the left endpoint 
.
The absolute
is 
, and it occurs at the right endpoint 
.
on the closed interval .A) The absolute
is , and it occurs at the left endpoint .The absolute
is , and it occurs at the right endpoint .B) The absolute
is , and it occurs at the right endpoint .The absolute
is , and it occurs at the left endpoint .C) The absolute
is , and it occurs at the left endpoint .The absolute
is , and it occurs at the right endpoint .D) The absolute
is , and it occurs at the right endpoint .The absolute
is and it occurs at the left endpoint .E) The absolute
is , and it occurs at the left endpoint .The absolute
is , and it occurs at the right endpoint . سؤال
Find the value of the derivative (if it exists) of 
at the indicated extremum. 
A)
is undefined.
B)
C)
D)
E)
at the indicated extremum. A)
is undefined.B)
C)
D)
E)
سؤال
Locate the absolute extrema of the function 
on the closed interval 
.
A) The absolute maximum is
, and it occurs at the critical number x = 0.
The absolute minimum is
, and it occurs at the left endpoint 
.
B) The absolute maximum is
, and it occurs at either endpoint 
.
The absolute minimum is 0, and it occurs at the critical number x = 0.
C) The absolute maximum is
, and it occurs only at the left endpoint 
.
The absolute minimum is 0 and it occurs at the critical number x = 0.
D) The absolute maximum is
, and it occurs at the critical number x = 0.
The absolute minimum is
, and it occurs at the right endpoint 
.
E) The absolute maximum is
, and it occurs only at the right endpoint 
The absolute minimum is 0 and it occurs at the critical number x = 0.
on the closed interval .A) The absolute maximum is
, and it occurs at the critical number x = 0.The absolute minimum is
, and it occurs at the left endpoint .B) The absolute maximum is
, and it occurs at either endpoint .The absolute minimum is 0, and it occurs at the critical number x = 0.
C) The absolute maximum is
, and it occurs only at the left endpoint .The absolute minimum is 0 and it occurs at the critical number x = 0.
D) The absolute maximum is
, and it occurs at the critical number x = 0.The absolute minimum is
, and it occurs at the right endpoint .E) The absolute maximum is
, and it occurs only at the right endpoint The absolute minimum is 0 and it occurs at the critical number x = 0.
سؤال
Locate the absolute extrema of the function 
on the closed interval 
.
A) absolute maximum:
Absolute minimum:
B) absolute maximum:
Absolute minimum:
C) absolute maximum:
Absolute minimum:
D) absolute maximum:
Absolute minimum:
E) absolute maximum:
Absolute minimum:
on the closed interval .A) absolute maximum:
Absolute minimum:
B) absolute maximum:
Absolute minimum:
C) absolute maximum:
Absolute minimum:
D) absolute maximum:
Absolute minimum:
E) absolute maximum:
Absolute minimum:
سؤال
Use a graphing utility to graph the function 
and locate the absolute extrema of the function on the interval 
.
A) left endpoint:
absolute minimum
Right endpoint:
absolute maximum
Critical points: none
B) left endpoint:
absolute minimum
Right endpoint:
absolute maximum
Critical points: none
C) left endpoint:
absolute minimum
Right endpoint:
Critical points:
absolute maximum
D) left endpoint:
absolute maximum
Right endpoint:
absolute minimum
Critical points: none
E) left endpoint:
absolute minimum
Right endpoint:
absolute maximum
Critical points:
and locate the absolute extrema of the function on the interval .A) left endpoint:
absolute minimumRight endpoint:
absolute maximumCritical points: none
B) left endpoint:
absolute minimumRight endpoint:
absolute maximumCritical points: none
C) left endpoint:
absolute minimumRight endpoint:
Critical points:
absolute maximumD) left endpoint:
absolute maximumRight endpoint:
absolute minimumCritical points: none
E) left endpoint:
absolute minimumRight endpoint:
absolute maximumCritical points:
سؤال
Find any critical numbers of the function 
.
A) 0
B)
C)
D)
E)
.A) 0
B)
C)
D)
E)
سؤال
Use a graphing utility to graph the function 
and locate the absolute extrema of the function on the interval 
.
A) absolute minimum:
No absolute maximum
B) absolute minimum:
No absolute maximum
C) absolute minimum:
No absolute maximum
D) absolute minimum:
Absolute maximum:
E) absolute maximum:
Absolute minimum:
and locate the absolute extrema of the function on the interval .A) absolute minimum:
No absolute maximum
B) absolute minimum:
No absolute maximum
C) absolute minimum:
No absolute maximum
D) absolute minimum:
Absolute maximum:
E) absolute maximum:
Absolute minimum:
سؤال
Find all critical numbers of the function 
, 
.
A)
B)
C)
D)
E)
, .A)
B)
C)
D)
E)
سؤال
Find the value of the derivative (if it exists) of the function 
at the extremum point 
. 
A)
B)
C)
D) 0
E) 1
at the extremum point . A)
B)
C)
D) 0
E) 1
سؤال
Find the value of the derivative (if it exists) of the function 
at the extremum point 
. 
A)
B) 0
C)
D)
E) does not exist
at the extremum point . A)
B) 0
C)
D)
E) does not exist
سؤال
Locate the absolute extrema of the given function on the closed interval 
. 
A) absolute max: (0, 0); absolute min
B) absolute max:
; absolute min (0, 0)
C) absolute max:
; absolute min 
D) absolute max:
; no absolute min
E) no absolute max; absolute min:
. A) absolute max: (0, 0); absolute min
B) absolute max:
; absolute min (0, 0)C) absolute max:
; absolute min D) absolute max:
; no absolute minE) no absolute max; absolute min:
سؤال
Locate the absolute extrema of the function 
on the closed interval 
.
A) absolute max: (0,1) ; absolute min:
B) absolute max:
; absolute min: (0, 1)
C) absolute max:
; no absolute min
D) no absolute max; absolute min: (0, 1)
E) absolute max: (0,1); no absolute min
on the closed interval .A) absolute max: (0,1) ; absolute min:
B) absolute max:
; absolute min: (0, 1)C) absolute max:
; no absolute minD) no absolute max; absolute min: (0, 1)
E) absolute max: (0,1); no absolute min
سؤال
Use a computer algebra system to graph the function 
and determine all absolute extrema on the interval 
.
A) absolute maximum:
Absolute minimum:
B) absolute maximum:
Absolute minimum:
C) absolute maximum:
Absolute minimum:
D) absolute maximum:
Absolute minimum:
E) absolute maximum:
Absolute minimum:
and determine all absolute extrema on the interval .A) absolute maximum:
Absolute minimum:
B) absolute maximum:
Absolute minimum:
C) absolute maximum:
Absolute minimum:
D) absolute maximum:
Absolute minimum:
E) absolute maximum:
Absolute minimum:
سؤال
Find all critical numbers of the function 
.
A) critical numbers:
B) critical numbers:
C) critical numbers:
D) critical numbers:
E) no critical numbers
.A) critical numbers:
B) critical numbers:
C) critical numbers:
D) critical numbers:
E) no critical numbers
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العب
ملء الشاشة (f)
Deck 4: Section 1 : Applications of Differentiation
1
Sketch the graph of the function and locate the absolute extrema of the function on the interval .
A) left endpoint: absolute minimum
Right endpoint: absolute maximum
B) left endpoint: absolute minimum
Right endpoint: absolute maximum
C) left endpoint: absolute minimum
Right endpoint: absolute maximum
D) left endpoint: absolute minimum
Right endpoint: absolute maximum
E) left endpoint: absolute minimum
Right endpoint: absolute maximum
and locate the absolute extrema of the function on the interval .A) left endpoint:
absolute minimumRight endpoint:
absolute maximumB) left endpoint:
absolute minimumRight endpoint:
absolute maximumC) left endpoint:
absolute minimumRight endpoint:
absolute maximumD) left endpoint:
absolute minimumRight endpoint:
absolute maximumE) left endpoint:
absolute minimumRight endpoint:
absolute maximumleft endpoint: absolute minimum
Right endpoint: absolute maximum
absolute minimumRight endpoint:
absolute maximum 2
Locate the absolute extrema of the function on the closed interval . Round your answers to four decimal places.
A) left endpoint:
Right endpoint: absolute maximum
Critical points: absolute minimum
B) left endpoint: absolute minimum
Right endpoint: absolute maximum
Critical points: none
C) left endpoint: absolute minimum
Right endpoint: absolute maximum
Critical points:
D) left endpoint: absolute minimum
Right endpoint: absolute maximum
Critical points: none
E) left endpoint:
Right endpoint: absolute maximum
Critical points: absolute minimum
on the closed interval . Round your answers to four decimal places.A) left endpoint:
Right endpoint:
absolute maximumCritical points:
absolute minimumB) left endpoint:
absolute minimumRight endpoint:
absolute maximumCritical points: none
C) left endpoint:
absolute minimumRight endpoint:
absolute maximumCritical points:
D) left endpoint:
absolute minimumRight endpoint:
absolute maximumCritical points: none
E) left endpoint:
Right endpoint:
absolute maximumCritical points:
absolute minimumleft endpoint:
Right endpoint: absolute maximum
Critical points: absolute minimum
Right endpoint:
absolute maximumCritical points:
absolute minimum 3
Locate the absolute extrema of the function on the closed interval .
A) absolute max: ; no absolute min
B) no absolute max or min
C) no absolute max; absolute min:
D) absolute max: ; absolute min:
E) absolute max: ; absolute min:
on the closed interval .A) absolute max:
; no absolute minB) no absolute max or min
C) no absolute max; absolute min:
D) absolute max:
; absolute min: E) absolute max:
; absolute min: absolute max: ; absolute min:
; absolute min: 4
Find all critical numbers of of the function , .
A)
B)
C)
D)
E)
, .A)
B)
C)
D)
E)
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5
Locate the absolute extrema of the function on the closed interval .
A) absolute max: ; absolute min:
B) no absolute max; absolute min:
C) absolute max: ; absolute min:
D) absolute max: ; no absolute min
E) no absolute max or min
on the closed interval .A) absolute max:
; absolute min: B) no absolute max; absolute min:
C) absolute max:
; absolute min: D) absolute max:
; no absolute minE) no absolute max or min
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6
Locate the absolute extrema of the function on the closed interval .
A) The absolute is , and it occurs at the left endpoint .
The absolute is , and it occurs at the right endpoint .
B) The absolute is , and it occurs at the right endpoint .
The absolute is , and it occurs at the left endpoint .
C) The absolute is , and it occurs at the left endpoint .
The absolute is , and it occurs at the right endpoint .
D) The absolute is , and it occurs at the right endpoint .
The absolute is and it occurs at the left endpoint .
E) The absolute is , and it occurs at the left endpoint .
The absolute is , and it occurs at the right endpoint .
on the closed interval .A) The absolute
is , and it occurs at the left endpoint .The absolute
is , and it occurs at the right endpoint .B) The absolute
is , and it occurs at the right endpoint .The absolute
is , and it occurs at the left endpoint .C) The absolute
is , and it occurs at the left endpoint .The absolute
is , and it occurs at the right endpoint .D) The absolute
is , and it occurs at the right endpoint .The absolute
is and it occurs at the left endpoint .E) The absolute
is , and it occurs at the left endpoint .The absolute
is , and it occurs at the right endpoint . فتح الحزمة
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7
Find the value of the derivative (if it exists) of at the indicated extremum.
A) is undefined.
B)
C)
D)
E)
at the indicated extremum. A)
is undefined.B)
C)
D)
E)
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8
Locate the absolute extrema of the function on the closed interval .
A) The absolute maximum is , and it occurs at the critical number x = 0.
The absolute minimum is , and it occurs at the left endpoint .
B) The absolute maximum is , and it occurs at either endpoint .
The absolute minimum is 0, and it occurs at the critical number x = 0.
C) The absolute maximum is , and it occurs only at the left endpoint .
The absolute minimum is 0 and it occurs at the critical number x = 0.
D) The absolute maximum is , and it occurs at the critical number x = 0.
The absolute minimum is , and it occurs at the right endpoint .
E) The absolute maximum is , and it occurs only at the right endpoint
The absolute minimum is 0 and it occurs at the critical number x = 0.
on the closed interval .A) The absolute maximum is
, and it occurs at the critical number x = 0.The absolute minimum is
, and it occurs at the left endpoint .B) The absolute maximum is
, and it occurs at either endpoint .The absolute minimum is 0, and it occurs at the critical number x = 0.
C) The absolute maximum is
, and it occurs only at the left endpoint .The absolute minimum is 0 and it occurs at the critical number x = 0.
D) The absolute maximum is
, and it occurs at the critical number x = 0.The absolute minimum is
, and it occurs at the right endpoint .E) The absolute maximum is
, and it occurs only at the right endpoint The absolute minimum is 0 and it occurs at the critical number x = 0.
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9
Locate the absolute extrema of the function on the closed interval .
A) absolute maximum:
Absolute minimum:
B) absolute maximum:
Absolute minimum:
C) absolute maximum:
Absolute minimum:
D) absolute maximum:
Absolute minimum:
E) absolute maximum:
Absolute minimum:
on the closed interval .A) absolute maximum:
Absolute minimum:
B) absolute maximum:
Absolute minimum:
C) absolute maximum:
Absolute minimum:
D) absolute maximum:
Absolute minimum:
E) absolute maximum:
Absolute minimum:
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10
Use a graphing utility to graph the function and locate the absolute extrema of the function on the interval .
A) left endpoint: absolute minimum
Right endpoint: absolute maximum
Critical points: none
B) left endpoint: absolute minimum
Right endpoint: absolute maximum
Critical points: none
C) left endpoint: absolute minimum
Right endpoint:
Critical points: absolute maximum
D) left endpoint: absolute maximum
Right endpoint: absolute minimum
Critical points: none
E) left endpoint: absolute minimum
Right endpoint: absolute maximum
Critical points:
and locate the absolute extrema of the function on the interval .A) left endpoint:
absolute minimumRight endpoint:
absolute maximumCritical points: none
B) left endpoint:
absolute minimumRight endpoint:
absolute maximumCritical points: none
C) left endpoint:
absolute minimumRight endpoint:
Critical points:
absolute maximumD) left endpoint:
absolute maximumRight endpoint:
absolute minimumCritical points: none
E) left endpoint:
absolute minimumRight endpoint:
absolute maximumCritical points:
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11
Find any critical numbers of the function .
A) 0
B)
C)
D)
E)
.A) 0
B)
C)
D)
E)
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12
Use a graphing utility to graph the function and locate the absolute extrema of the function on the interval .
A) absolute minimum:
No absolute maximum
B) absolute minimum:
No absolute maximum
C) absolute minimum:
No absolute maximum
D) absolute minimum:
Absolute maximum:
E) absolute maximum:
Absolute minimum:
and locate the absolute extrema of the function on the interval .A) absolute minimum:
No absolute maximum
B) absolute minimum:
No absolute maximum
C) absolute minimum:
No absolute maximum
D) absolute minimum:
Absolute maximum:
E) absolute maximum:
Absolute minimum:
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13
Find all critical numbers of the function , .
A)
B)
C)
D)
E)
, .A)
B)
C)
D)
E)
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14
Find the value of the derivative (if it exists) of the function at the extremum point .
A)
B)
C)
D) 0
E) 1
at the extremum point . A)
B)
C)
D) 0
E) 1
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15
Find the value of the derivative (if it exists) of the function at the extremum point .
A)
B) 0
C)
D)
E) does not exist
at the extremum point . A)
B) 0
C)
D)
E) does not exist
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16
Locate the absolute extrema of the given function on the closed interval .
A) absolute max: (0, 0); absolute min
B) absolute max: ; absolute min (0, 0)
C) absolute max: ; absolute min
D) absolute max: ; no absolute min
E) no absolute max; absolute min:
. A) absolute max: (0, 0); absolute min
B) absolute max:
; absolute min (0, 0)C) absolute max:
; absolute min D) absolute max:
; no absolute minE) no absolute max; absolute min:
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17
Locate the absolute extrema of the function on the closed interval .
A) absolute max: (0,1) ; absolute min:
B) absolute max: ; absolute min: (0, 1)
C) absolute max: ; no absolute min
D) no absolute max; absolute min: (0, 1)
E) absolute max: (0,1); no absolute min
on the closed interval .A) absolute max: (0,1) ; absolute min:
B) absolute max:
; absolute min: (0, 1)C) absolute max:
; no absolute minD) no absolute max; absolute min: (0, 1)
E) absolute max: (0,1); no absolute min
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18
Use a computer algebra system to graph the function and determine all absolute extrema on the interval .
A) absolute maximum:
Absolute minimum:
B) absolute maximum:
Absolute minimum:
C) absolute maximum:
Absolute minimum:
D) absolute maximum:
Absolute minimum:
E) absolute maximum:
Absolute minimum:
and determine all absolute extrema on the interval .A) absolute maximum:
Absolute minimum:
B) absolute maximum:
Absolute minimum:
C) absolute maximum:
Absolute minimum:
D) absolute maximum:
Absolute minimum:
E) absolute maximum:
Absolute minimum:
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19
Find all critical numbers of the function .
A) critical numbers:
B) critical numbers:
C) critical numbers:
D) critical numbers:
E) no critical numbers
.A) critical numbers:
B) critical numbers:
C) critical numbers:
D) critical numbers:
E) no critical numbers
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