Find the location of the maxima, minima, and saddle points of f(x,y), if any, given the partial derivatives below. Describe your reasoning in each case. a. fy = 3x - 4y and f, = 3y - 4x b. fy = 4x - 8 and fy = 2y -6 c. fy = 7x2 - 7 and fy = 2y +2 Are there any local minima? 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 value(s) of fyx at this/these point(s) is/are and the value(s) of fyxfyy - fy at this/these point(s) is/are (Type an exact answer. Use a comma to separate answers as needed.) B. There are no local minima. Are there any saddle points? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. A saddle point occurs at (Type an ordered pair. Use a comma to separate answers as needed.) The value(s) of fyyfw - f, at this/these point(s) is/are (Simplify your answers. Use a comma to separate answers as needed.) O B. There are no saddle points.
Find the location of the maxima, minima, and saddle points of f(x,y), if any, given the partial derivatives below. Describe your reasoning in each case. a. fy = 3x - 4y and f, = 3y - 4x b. fy = 4x - 8 and fy = 2y -6 c. fy = 7x2 - 7 and fy = 2y +2 Are there any local minima? 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 value(s) of fyx at this/these point(s) is/are and the value(s) of fyxfyy - fy at this/these point(s) is/are (Type an exact answer. Use a comma to separate answers as needed.) B. There are no local minima. Are there any saddle points? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. A saddle point occurs at (Type an ordered pair. Use a comma to separate answers as needed.) The value(s) of fyyfw - f, at this/these point(s) is/are (Simplify your answers. 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
Problem 1RQ
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Find the location of the
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Transcribed Image Text:Find the location of the maxima, minima, and saddle points of f(x,y), if any, given the partial derivatives below. Describe your reasoning in each case.
a. fy = 3x - 4y and f, = 3y - 4x
b. fy = 4x - 8 and fy = 2y -6
c. fy = 7x2 - 7 and fy = 2y +2
Are there any local minima? 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 value(s) of fyx at this/these point(s) is/are
and the value(s) of fyxfyy - fy at this/these point(s) is/are
(Type an exact answer. Use a comma to separate answers as needed.)
B. There are no local minima.
Are there any saddle points? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
O A. A saddle point occurs at
(Type an ordered pair. Use a comma to separate answers as needed.)
The value(s) of fyyfw - f, at this/these point(s) is/are
(Simplify your answers. Use a comma to separate answers as needed.)
O B. There are no saddle points.
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