25 Find all the local maxima, local minima, and saddle points of the function. f(x,y) = x2 + xy + y? + 2x - 2y +2 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. A local maximum occurs at (Type an ordered pair. Use a comma to separate answers as needed.) The local maximum value(s) is/are (Type an exact answer. Use comma to separate answers as needed.) O B. There are no local maxima. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. A local minimum occurs at (Type an ordered pair. Use a comma to separate answers as needed.) The local minimum value(s) is/are (Type an exact answer. Use a comma to separate answers as needed.) O B. There are no local minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. A saddle point occurs at (Type an ordered pair. Use a comma to separate answers as needed.) O B. There are no saddle points.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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23
Find all the local maxima, local minima, and saddle points of the function.
23
f(x,y) = x2 + xy + y² + 2x - 2y +2
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
O A. A local maximum occurs at
(Type an ordered pair. Use a comma to separate answers as needed.)
The local maximum value(s) is/are.
(Type an exact answer. Use
comma to separate answers as needed.)
O B. There are no local maxima.
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
O A. A local minimum occurs at
(Type an ordered pair. Use a comma to separate answers as needed.)
The local minimum value(s) is/are
(Type an exact answer, Use
comma to separate answers as needed.)
O B. There are no local minima.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. A saddle point occurs at
(Type an ordered pair. Use a comma to separate answers as needed.)
O B. There are no saddle points.
Transcribed Image Text:Find all the local maxima, local minima, and saddle points of the function. 23 f(x,y) = x2 + xy + y² + 2x - 2y +2 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. A local maximum occurs at (Type an ordered pair. Use a comma to separate answers as needed.) The local maximum value(s) is/are. (Type an exact answer. Use comma to separate answers as needed.) O B. There are no local maxima. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. A local minimum occurs at (Type an ordered pair. Use a comma to separate answers as needed.) The local minimum value(s) is/are (Type an exact answer, Use comma to separate answers as needed.) O B. There are no local minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. A saddle point occurs at (Type an ordered pair. Use a comma to separate answers as needed.) O B. There are no saddle points.
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