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Show that (0,0) is a critical point of f(x,y) = x2 + kxy + y2 no matter what value the constant k has. Choose the correct definition of a critical point below. A. A critical point occurs when f, = f, # 0. B. A critical point occurs either when f, = f, = 0, or when f, or f, fails to exist. O C. A critical point occurs either when fy = fw = 0, or when fy or f, fails to exist. 'xx 'yy 'xx 'yy O D. A critical point occurs when fyx = fy #0. Determine f,. fx %3D Determine f,. Evaluate f, at (0,0). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. f<(0,0) = (Type an expression using k as the variable. Simplify your answer.) B. f(0,0) does not exist. Evaluate f, at (0,0). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. f,(0,0) = (Type an expression using k as the variable. Simplify your answer.) B. fy(0,0) does not exist.

Show that (0,0) is a critical point of f(x,y) = x2 + kxy + y2 no matter what value the constant k has. Choose the correct definition of a critical point below. A. A critical point occurs when f, = f, # 0. B. A critical point occurs either when f, = f, = 0, or when f, or f, fails to exist. O C. A critical point occurs either when fy = fw = 0, or when fy or f, fails to exist. 'xx 'yy 'xx 'yy O D. A critical point occurs when fyx = fy #0. Determine f,. fx %3D Determine f,. Evaluate f, at (0,0). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. f<(0,0) = (Type an expression using k as the variable. Simplify your answer.) B. f(0,0) does not exist. Evaluate f, at (0,0). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. f,(0,0) = (Type an expression using k as the variable. Simplify your answer.) B. fy(0,0) does not exist.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Show that (0,0) is a critical point of f(x,y) = x2 + kxy + y2 no matter what value the constant k has. Choose the correct definition of a critical point below. A. A critical point occurs when f, = f, # 0. B. A critical point occurs either when f, = f, = 0, or when f, or f, fails to exist. O C. A critical point occurs either when fy = fw = 0, or when fy or f, fails to exist. 'xx 'yy 'xx 'yy O D. A critical point occurs when fyx = fy #0. Determine f,. fx %3D Determine f,. Evaluate f, at (0,0). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. f<(0,0) = (Type an expression using k as the variable. Simplify your answer.) B. f(0,0) does not exist. Evaluate f, at (0,0). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. f,(0,0) = (Type an expression using k as the variable. Simplify your answer.) B. fy(0,0) does not exist.
Transcribed Image Text:Show that (0,0) is a critical point of f(x,y) = x2 + kxy + y2 no matter what value the constant k has. Choose the correct definition of a critical point below. A. A critical point occurs when f, = f, # 0. B. A critical point occurs either when f, = f, = 0, or when f, or f, fails to exist. O C. A critical point occurs either when fy = fw = 0, or when fy or f, fails to exist. 'xx 'yy 'xx 'yy O D. A critical point occurs when fyx = fy #0. Determine f,. fx %3D Determine f,. Evaluate f, at (0,0). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. f<(0,0) = (Type an expression using k as the variable. Simplify your answer.) B. f(0,0) does not exist. Evaluate f, at (0,0). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. f,(0,0) = (Type an expression using k as the variable. Simplify your answer.) B. fy(0,0) does not exist.
Find all the local maxima, local minima, and saddle points of the function shown below. 7 f(x,y) = 9 - Vx2 +y? Find the local maxima. Select the correct choice below and, if necessary, fill in the answer boxes as needed 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 a comma to separate answers as needed.) O B. There are no local maxima. Find the local minima. Select the correct choice below and, if necessary, fill in the answer boxes as needed 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.) B. There are no local minima. Find the saddle points. Select the correct choice below and, if necessary, fill in the answer box as needed to complete your choice. A. A saddle point occurs at (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no saddle points.
Transcribed Image Text:Find all the local maxima, local minima, and saddle points of the function shown below. 7 f(x,y) = 9 - Vx2 +y? Find the local maxima. Select the correct choice below and, if necessary, fill in the answer boxes as needed 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 a comma to separate answers as needed.) O B. There are no local maxima. Find the local minima. Select the correct choice below and, if necessary, fill in the answer boxes as needed 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.) B. There are no local minima. Find the saddle points. Select the correct choice below and, if necessary, fill in the answer box as needed to complete your choice. A. A saddle point occurs at (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no saddle points.
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