The function f has continuous second derivatives, and a critical point at (-4, 6). Suppose fxx(−4, 6) = −8, fxy(−4, 6) = −8, fyy(−4, 6) = 2. Then the point (-4, 6): O A. cannot be determined B. is a local maximum C. is a saddle point OD. is a local minimum OE. None of the above
The function f has continuous second derivatives, and a critical point at (-4, 6). Suppose fxx(−4, 6) = −8, fxy(−4, 6) = −8, fyy(−4, 6) = 2. Then the point (-4, 6): O A. cannot be determined B. is a local maximum C. is a saddle point OD. is a local minimum OE. None of the above
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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I need help with this question! My answer "B" was wrong and do not know the answer. Thank you in advance!
![The function \( f \) has continuous second derivatives, and a critical point at \((-4, 6)\). Suppose
\[
f_{xx}(-4, 6) = -8, \quad f_{xy}(-4, 6) = -8, \quad f_{yy}(-4, 6) = 2.
\]
Then the point \((-4, 6)\):
- A. cannot be determined
- B. is a local maximum
- C. is a saddle point
- D. is a local minimum
- E. None of the above
The correct answer is:
- B. is a local maximum](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1858a710-c111-4513-9004-6c10bf7d1d6e%2Ff057d585-3e6c-48ce-b6a9-f9ef2ff36dae%2Fxhlkts_processed.png&w=3840&q=75)
Transcribed Image Text:The function \( f \) has continuous second derivatives, and a critical point at \((-4, 6)\). Suppose
\[
f_{xx}(-4, 6) = -8, \quad f_{xy}(-4, 6) = -8, \quad f_{yy}(-4, 6) = 2.
\]
Then the point \((-4, 6)\):
- A. cannot be determined
- B. is a local maximum
- C. is a saddle point
- D. is a local minimum
- E. None of the above
The correct answer is:
- B. is a local maximum
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