تكلم مع الذكاء الاصطناعي
Deck 11: Extension G: Partial Derivatives
ملء الشاشة (f)
سؤال
Find and classify the relative extrema and saddle points of the function 
for 
and 
A) Relative maximum
B) Saddle point
C) Relative minimum
D) None
for and A) Relative maximum
B) Saddle point
C) Relative minimum
D) None
سؤال
Suppose (1,1)is a critical point of a function f with continuous second derivatives. In the case of 
, 
, 
what can you say about f ?
A) f has a saddle point at (1,1)
B) f has a local minimum at (1,1)
C) f has a local maximum at (1,1)
, , what can you say about f ?A) f has a saddle point at (1,1)
B) f has a local minimum at (1,1)
C) f has a local maximum at (1,1)
سؤال
Find the critical points of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the points on the surface 
that are closest to the origin.
A)
B)
C)
D)
E)
that are closest to the origin.A)
B)
C)
D)
E)
سؤال
Find the absolute extrema of the function 
on the closed triangular region with vertices 
, 
and 
A) Absolute minimum 5, Absolute maximum 17
B) Absolute minimum 0, Absolute maximum 5
C) Absolute minimum -5, Absolute maximum 5
D) Absolute minimum -5, Absolute maximum 17
on the closed triangular region with vertices , and A) Absolute minimum 5, Absolute maximum 17
B) Absolute minimum 0, Absolute maximum 5
C) Absolute minimum -5, Absolute maximum 5
D) Absolute minimum -5, Absolute maximum 17
سؤال
Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is 
A)
, 
, 
B) 4, 8, 16
C) 32,
, 16
D)
, 
, 
E) 32, 32, 32
A)
, , B) 4, 8, 16
C) 32,
, 16D)
, , E) 32, 32, 32
سؤال
Find the local maximum,and minimum value and saddle points of the function. 
سؤال
Find the absolute minimum value of the function 
on the set D.D is the region bounded by the parabola 
and the line 
A) 0
B)
C)
D)
E) 30
on the set D.D is the region bounded by the parabola and the line A) 0
B)
C)
D)
E) 30
سؤال
A cardboard box without a lid is to have a volume of 
cm 
Find the dimensions that minimize the amount of cardboard used.
cm Find the dimensions that minimize the amount of cardboard used. سؤال
Find three positive numbers whose sum is 
and whose product is a maximum.
and whose product is a maximum. سؤال
Find three positive numbers whose sum is 
and whose product is a maximum.
A)
B)
C)
D)
E)
and whose product is a maximum.A)
B)
C)
D)
E)
سؤال
Find the shortest distance from the point 
to the plane 
A)
B)
C)
D)
E)
to the plane A)
B)
C)
D)
E)
سؤال
Find the dimensions of the rectangular box with largest volume if the total surface area is given as 
A) 21 cm, 14 cm, 1.75 cm
B) 14cm, 1.75 cm, 1.75 cm
C) 7 cm, 7 cm, 7cm
D) 294 cm, 7 cm, 7cm
E) 14 cm, 14 cm, 3.5 cm
A) 21 cm, 14 cm, 1.75 cm
B) 14cm, 1.75 cm, 1.75 cm
C) 7 cm, 7 cm, 7cm
D) 294 cm, 7 cm, 7cm
E) 14 cm, 14 cm, 3.5 cm
سؤال
Find and classify the relative extrema and saddle points of the function 
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العب
ملء الشاشة (f)
Deck 11: Extension G: Partial Derivatives
1
Find and classify the relative extrema and saddle points of the function for and
A) Relative maximum
B) Saddle point
C) Relative minimum
D) None
for and A) Relative maximum
B) Saddle point
C) Relative minimum
D) None
None
2
Suppose (1,1)is a critical point of a function f with continuous second derivatives. In the case of , , what can you say about f ?
A) f has a saddle point at (1,1)
B) f has a local minimum at (1,1)
C) f has a local maximum at (1,1)
, , what can you say about f ?A) f has a saddle point at (1,1)
B) f has a local minimum at (1,1)
C) f has a local maximum at (1,1)
f has a local minimum at (1,1)
3
Find the critical points of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Find the points on the surface that are closest to the origin.
A)
B)
C)
D)
E)
that are closest to the origin.A)
B)
C)
D)
E)
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5
Find the absolute extrema of the function on the closed triangular region with vertices , and
A) Absolute minimum 5, Absolute maximum 17
B) Absolute minimum 0, Absolute maximum 5
C) Absolute minimum -5, Absolute maximum 5
D) Absolute minimum -5, Absolute maximum 17
on the closed triangular region with vertices , and A) Absolute minimum 5, Absolute maximum 17
B) Absolute minimum 0, Absolute maximum 5
C) Absolute minimum -5, Absolute maximum 5
D) Absolute minimum -5, Absolute maximum 17
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 14 في هذه المجموعة.
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6
Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is
A) , ,
B) 4, 8, 16
C) 32, , 16
D) , ,
E) 32, 32, 32
A)
, , B) 4, 8, 16
C) 32,
, 16D)
, , E) 32, 32, 32
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 14 في هذه المجموعة.
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7
Find the local maximum,and minimum value and saddle points of the function.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 14 في هذه المجموعة.
فتح الحزمة
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8
Find the absolute minimum value of the function on the set D.D is the region bounded by the parabola and the line
A) 0
B)
C)
D)
E) 30
on the set D.D is the region bounded by the parabola and the line A) 0
B)
C)
D)
E) 30
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 14 في هذه المجموعة.
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9
A cardboard box without a lid is to have a volume of cm Find the dimensions that minimize the amount of cardboard used.
cm Find the dimensions that minimize the amount of cardboard used. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 14 في هذه المجموعة.
فتح الحزمة
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10
Find three positive numbers whose sum is and whose product is a maximum.
and whose product is a maximum. فتح الحزمة
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11
Find three positive numbers whose sum is and whose product is a maximum.
A)
B)
C)
D)
E)
and whose product is a maximum.A)
B)
C)
D)
E)
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12
Find the shortest distance from the point to the plane
A)
B)
C)
D)
E)
to the plane A)
B)
C)
D)
E)
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افتح القفل للوصول البطاقات البالغ عددها 14 في هذه المجموعة.
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13
Find the dimensions of the rectangular box with largest volume if the total surface area is given as
A) 21 cm, 14 cm, 1.75 cm
B) 14cm, 1.75 cm, 1.75 cm
C) 7 cm, 7 cm, 7cm
D) 294 cm, 7 cm, 7cm
E) 14 cm, 14 cm, 3.5 cm
A) 21 cm, 14 cm, 1.75 cm
B) 14cm, 1.75 cm, 1.75 cm
C) 7 cm, 7 cm, 7cm
D) 294 cm, 7 cm, 7cm
E) 14 cm, 14 cm, 3.5 cm
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14
Find and classify the relative extrema and saddle points of the function
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 14 في هذه المجموعة.
فتح الحزمة
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