Chat with AI
Deck 13: Section 9: Functions of Several Variables
Full screen (f)
Question
Examine the function 
for relative extrema and saddle points. 
A) relative minimum:
B) relative minimum:
C) relative maximum:
D) saddle point:
E) saddle point:
for relative extrema and saddle points. A) relative minimum:
B) relative minimum:
C) relative maximum:
D) saddle point:
E) saddle point:
Question
Find the critical points of the function 
, and from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.
A) relative maxima at
, 
, 
, where 
are arbitrary real numbers
B) relative minima at
, 
, 
, where 
are arbitrary real numbers
C) relative minimum at
D) relative maximum at
E) no relative extrema
, and from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.A) relative maxima at
, , , where are arbitrary real numbersB) relative minima at
, , , where are arbitrary real numbersC) relative minimum at
D) relative maximum at
E) no relative extrema
Question
Examine the function 
for relative extrema and saddle points.
A) saddle point:
B) relative minimum:
C) relative minimum:
D) saddle point:
E) saddle point:
for relative extrema and saddle points.A) saddle point:
B) relative minimum:
C) relative minimum:
D) saddle point:
E) saddle point:
Question
Examine the function 
for relative extrema and saddle points. 
A) saddle point:
B) relative minimum:
C) relative maximum:
D) relative minimum:
E) no critical points
for relative extrema and saddle points. A) saddle point:
B) relative minimum:
C) relative maximum:
D) relative minimum:
E) no critical points
Question
Find the critical points of the function 
, and from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.
A) relative minimum at
B) relative maximum at
C) relative maximum at
D) relative minimum at
E) no relative extrema
, and from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.A) relative minimum at
B) relative maximum at
C) relative maximum at
D) relative minimum at
E) no relative extrema
Question
Examine the function 
for relative extrema.
A) relative minimum:
B) relative minimum:
C) relative maximum:
D) relative maximum:
E) no relative extrema
for relative extrema.A) relative minimum:
B) relative minimum:
C) relative maximum:
D) relative maximum:
E) no relative extrema
Question
List the critical points of the function 
for which the Second Partial Test fails.
A) Test fails at
and 
.
B) Test fails only at
.
C) Test fails at
.
D) Test fails at
.
E) Test fails only at
.
for which the Second Partial Test fails.A) Test fails at
and .B) Test fails only at
.C) Test fails at
.D) Test fails at
.E) Test fails only at
. Question
Examine the function 
for relative extrema.
A) relative maximum:
B) relative minimum:
C) relative maximum:
D) relative minimum:
E) no relative extrema
for relative extrema.A) relative maximum:
B) relative minimum:
C) relative maximum:
D) relative minimum:
E) no relative extrema
Question
Identify any extrema of the function 
by recognizing its given form or its form after completing the square.
A) relative maximum:
B) relative minimum:
C) relative minimum:
D) relative maximum:
E) relative maximum:
by recognizing its given form or its form after completing the square.A) relative maximum:
B) relative minimum:
C) relative minimum:
D) relative maximum:
E) relative maximum:
Question
Find the absolute extrema of 
on the region bounded by the square with vertices 
A) absolute minimum:
Absolute maximum:
B) absolute minimum:
Absolute maximum:
C) absolute minimum:
Absolute maximum:
D) absolute minimum:
Absolute maximum:
E) absolute minimum:
Absolute maximum:
on the region bounded by the square with vertices A) absolute minimum:
Absolute maximum:
B) absolute minimum:
Absolute maximum:
C) absolute minimum:
Absolute maximum:
D) absolute minimum:
Absolute maximum:
E) absolute minimum:
Absolute maximum:
Question
Examine the function 
for relative extrema.
A) relative minimum:
B) relative maximum:
C) relative maximum:
D) relative maximum:
E) relative minimum:
for relative extrema.A) relative minimum:
B) relative maximum:
C) relative maximum:
D) relative maximum:
E) relative minimum:
Question
Identify any extrema of the function 
by recognizing its given form or its form after completing the square.
A) relative maximum:
B) relative maximum:
C) relative minimum:
D) relative minimum:
E) relative maximum:
by recognizing its given form or its form after completing the square.A) relative maximum:
B) relative maximum:
C) relative minimum:
D) relative minimum:
E) relative maximum:
Question
Examine the function 
for relative extrema.
A) relative minimum:
B) relative maximum:
C) relative minimum:
D) relative minimum:
E) relative maximum:
for relative extrema.A) relative minimum:
B) relative maximum:
C) relative minimum:
D) relative minimum:
E) relative maximum:
Question
Find the absolute extrema of 
on the region 
.
A) absolute minimum:
Absolute maximum:
B) absolute minimum:
Absolute maximum:
C) absolute minimum:
Absolute maximum:
D) absolute minimum:
Absolute maximum:
E) absolute minimum:
Absolute maximum:
on the region .A) absolute minimum:
Absolute maximum:
B) absolute minimum:
Absolute maximum:
C) absolute minimum:
Absolute maximum:
D) absolute minimum:
Absolute maximum:
E) absolute minimum:
Absolute maximum:
Question
Find the absolute extrema of the function 
over the triangular region in the xy-plane with vertices 
.
A) absolute maximum:
at 
Absolute minimum:
at 
and along the line 
B) absolute maximum:
at 
Absolute minimum:
at 
and along the line 
C) absolute maximum:
at 
Absolute minimum:
at 
and along the line 
D) absolute maximum:
at 
Absolute minimum:
at 
E) absolute maximum:
at 
Absolute minimum:
at 
over the triangular region in the xy-plane with vertices .A) absolute maximum:
at Absolute minimum:
at and along the line B) absolute maximum:
at Absolute minimum:
at and along the line C) absolute maximum:
at Absolute minimum:
at and along the line D) absolute maximum:
at Absolute minimum:
at E) absolute maximum:
at Absolute minimum:
at Question
Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function 
at the critical point 
, if 
.
A) relative maximum
B) relative minimum
C) saddle point
D) insufficient information
at the critical point , if .A) relative maximum
B) relative minimum
C) saddle point
D) insufficient information
Question
Examine the function 
for relative extrema and saddle points.
A) saddle point:
; relative minimum: 
B) saddle point:
; relative minimum: 
C) relative minimum:
; relative maximum: 
D) relative minimum:
; relative maximum: 
E) saddle points:
, 
for relative extrema and saddle points.A) saddle point:
; relative minimum: B) saddle point:
; relative minimum: C) relative minimum:
; relative maximum: D) relative minimum:
; relative maximum: E) saddle points:
, 
Unlock Deck
Sign up to unlock the cards in this deck!
Unlock Deck
Unlock Deck
1/17
Play
Full screen (f)
Deck 13: Section 9: Functions of Several Variables
1
Examine the function for relative extrema and saddle points.
A) relative minimum:
B) relative minimum:
C) relative maximum:
D) saddle point:
E) saddle point:
for relative extrema and saddle points. A) relative minimum:
B) relative minimum:
C) relative maximum:
D) saddle point:
E) saddle point:
saddle point:
2
Find the critical points of the function , and from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.
A) relative maxima at , , , where are arbitrary real numbers
B) relative minima at , , , where are arbitrary real numbers
C) relative minimum at
D) relative maximum at
E) no relative extrema
, and from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.A) relative maxima at
, , , where are arbitrary real numbersB) relative minima at
, , , where are arbitrary real numbersC) relative minimum at
D) relative maximum at
E) no relative extrema
relative maxima at , , , where are arbitrary real numbers
, , , where are arbitrary real numbers 3
Examine the function for relative extrema and saddle points.
A) saddle point:
B) relative minimum:
C) relative minimum:
D) saddle point:
E) saddle point:
for relative extrema and saddle points.A) saddle point:
B) relative minimum:
C) relative minimum:
D) saddle point:
E) saddle point:
saddle point:
4
Examine the function for relative extrema and saddle points.
A) saddle point:
B) relative minimum:
C) relative maximum:
D) relative minimum:
E) no critical points
for relative extrema and saddle points. A) saddle point:
B) relative minimum:
C) relative maximum:
D) relative minimum:
E) no critical points
Unlock Deck
Unlock for access to all 17 flashcards in this deck.
Unlock Deck
k this deck
5
Find the critical points of the function , and from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.
A) relative minimum at
B) relative maximum at
C) relative maximum at
D) relative minimum at
E) no relative extrema
, and from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.A) relative minimum at
B) relative maximum at
C) relative maximum at
D) relative minimum at
E) no relative extrema
Unlock Deck
Unlock for access to all 17 flashcards in this deck.
Unlock Deck
k this deck
6
Examine the function for relative extrema.
A) relative minimum:
B) relative minimum:
C) relative maximum:
D) relative maximum:
E) no relative extrema
for relative extrema.A) relative minimum:
B) relative minimum:
C) relative maximum:
D) relative maximum:
E) no relative extrema
Unlock Deck
Unlock for access to all 17 flashcards in this deck.
Unlock Deck
k this deck
7
List the critical points of the function for which the Second Partial Test fails.
A) Test fails at and .
B) Test fails only at .
C) Test fails at .
D) Test fails at .
E) Test fails only at .
for which the Second Partial Test fails.A) Test fails at
and .B) Test fails only at
.C) Test fails at
.D) Test fails at
.E) Test fails only at
. Unlock Deck
Unlock for access to all 17 flashcards in this deck.
Unlock Deck
k this deck
8
Examine the function for relative extrema.
A) relative maximum:
B) relative minimum:
C) relative maximum:
D) relative minimum:
E) no relative extrema
for relative extrema.A) relative maximum:
B) relative minimum:
C) relative maximum:
D) relative minimum:
E) no relative extrema
Unlock Deck
Unlock for access to all 17 flashcards in this deck.
Unlock Deck
k this deck
9
Identify any extrema of the function by recognizing its given form or its form after completing the square.
A) relative maximum:
B) relative minimum:
C) relative minimum:
D) relative maximum:
E) relative maximum:
by recognizing its given form or its form after completing the square.A) relative maximum:
B) relative minimum:
C) relative minimum:
D) relative maximum:
E) relative maximum:
Unlock Deck
Unlock for access to all 17 flashcards in this deck.
Unlock Deck
k this deck
10
Find the absolute extrema of on the region bounded by the square with vertices
A) absolute minimum:
Absolute maximum:
B) absolute minimum:
Absolute maximum:
C) absolute minimum:
Absolute maximum:
D) absolute minimum:
Absolute maximum:
E) absolute minimum:
Absolute maximum:
on the region bounded by the square with vertices A) absolute minimum:
Absolute maximum:
B) absolute minimum:
Absolute maximum:
C) absolute minimum:
Absolute maximum:
D) absolute minimum:
Absolute maximum:
E) absolute minimum:
Absolute maximum:
Unlock Deck
Unlock for access to all 17 flashcards in this deck.
Unlock Deck
k this deck
11
Examine the function for relative extrema.
A) relative minimum:
B) relative maximum:
C) relative maximum:
D) relative maximum:
E) relative minimum:
for relative extrema.A) relative minimum:
B) relative maximum:
C) relative maximum:
D) relative maximum:
E) relative minimum:
Unlock Deck
Unlock for access to all 17 flashcards in this deck.
Unlock Deck
k this deck
12
Identify any extrema of the function by recognizing its given form or its form after completing the square.
A) relative maximum:
B) relative maximum:
C) relative minimum:
D) relative minimum:
E) relative maximum:
by recognizing its given form or its form after completing the square.A) relative maximum:
B) relative maximum:
C) relative minimum:
D) relative minimum:
E) relative maximum:
Unlock Deck
Unlock for access to all 17 flashcards in this deck.
Unlock Deck
k this deck
13
Examine the function for relative extrema.
A) relative minimum:
B) relative maximum:
C) relative minimum:
D) relative minimum:
E) relative maximum:
for relative extrema.A) relative minimum:
B) relative maximum:
C) relative minimum:
D) relative minimum:
E) relative maximum:
Unlock Deck
Unlock for access to all 17 flashcards in this deck.
Unlock Deck
k this deck
14
Find the absolute extrema of on the region .
A) absolute minimum:
Absolute maximum:
B) absolute minimum:
Absolute maximum:
C) absolute minimum:
Absolute maximum:
D) absolute minimum:
Absolute maximum:
E) absolute minimum:
Absolute maximum:
on the region .A) absolute minimum:
Absolute maximum:
B) absolute minimum:
Absolute maximum:
C) absolute minimum:
Absolute maximum:
D) absolute minimum:
Absolute maximum:
E) absolute minimum:
Absolute maximum:
Unlock Deck
Unlock for access to all 17 flashcards in this deck.
Unlock Deck
k this deck
15
Find the absolute extrema of the function over the triangular region in the xy-plane with vertices .
A) absolute maximum: at
Absolute minimum: at and along the line
B) absolute maximum: at
Absolute minimum: at and along the line
C) absolute maximum: at
Absolute minimum: at and along the line
D) absolute maximum: at
Absolute minimum: at
E) absolute maximum: at
Absolute minimum: at
over the triangular region in the xy-plane with vertices .A) absolute maximum:
at Absolute minimum:
at and along the line B) absolute maximum:
at Absolute minimum:
at and along the line C) absolute maximum:
at Absolute minimum:
at and along the line D) absolute maximum:
at Absolute minimum:
at E) absolute maximum:
at Absolute minimum:
at Unlock Deck
Unlock for access to all 17 flashcards in this deck.
Unlock Deck
k this deck
16
Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function at the critical point , if .
A) relative maximum
B) relative minimum
C) saddle point
D) insufficient information
at the critical point , if .A) relative maximum
B) relative minimum
C) saddle point
D) insufficient information
Unlock Deck
Unlock for access to all 17 flashcards in this deck.
Unlock Deck
k this deck
17
Examine the function for relative extrema and saddle points.
A) saddle point: ; relative minimum:
B) saddle point: ; relative minimum:
C) relative minimum: ; relative maximum:
D) relative minimum: ; relative maximum:
E) saddle points: ,
for relative extrema and saddle points.A) saddle point:
; relative minimum: B) saddle point:
; relative minimum: C) relative minimum:
; relative maximum: D) relative minimum:
; relative maximum: E) saddle points:
, Unlock Deck
Unlock for access to all 17 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 17 flashcards in this deck.
