Find the local extrema of the following function. f(x,y) = x³ - 3xy² +12y² For the critical points that do not fail the second-derivative test, determine whether these points are local maxima, lo minima, or saddle points. Select the correct choice below and fill in the answer box to complete your choice. (Type an ordered pair. Use a comma to separate answers as needed.) A. The function has (a) local minimum/minima at (x,y) = . B. The function has (a) local maximum/maxima at (x,y)= C. There is/are (a) saddle point(s) at (x,y)=¯. Does the second-derivative test for local extrema fail at any of the critical points? Select the correct choice below ar necessary, fill in the answer box to complete your choice. (Type an ordered pair. Use a comma to separate answers as needed.) O A. The second-derivative test for local extrema fails at (x,y)= B. The second-derivative test for local extrema does not fail for any of the critical points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Find the local extrema of the following function. f(x,y) = x³ - 3xy² +12y² For the critical points that do not fail the second-derivative test, determine whether these points are local maxima, lo minima, or saddle points. Select the correct choice below and fill in the answer box to complete your choice. (Type an ordered pair. Use a comma to separate answers as needed.) A. The function has (a) local minimum/minima at (x,y) = . B. The function has (a) local maximum/maxima at (x,y)= C. There is/are (a) saddle point(s) at (x,y)=¯. Does the second-derivative test for local extrema fail at any of the critical points? Select the correct choice below ar necessary, fill in the answer box to complete your choice. (Type an ordered pair. Use a comma to separate answers as needed.) O A. The second-derivative test for local extrema fails at (x,y)= B. The second-derivative test for local extrema does not fail for any of the critical points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
Related questions
Question
Transcribed Image Text:Find the local extrema of the following function.
f(x,y) = x³ - 3xy² +12y²
For the critical points that do not fail the second-derivative test, determine whether these points are local maxima, local
minima, or saddle points. Select the correct choice below and fill in the answer box to complete your choice.
(Type an ordered pair. Use a comma to separate answers as needed.)
O A. The function has (a) local minimum/minima at (x,y) =
B. The function has (a) local maximum/maxima at (x,y) = .
O c. There is/are (a) saddle point(s) at (x,y)=
Does the second-derivative test for local extrema fail at any of the critical points? Select the correct choice below and, if
necessary, fill in the answer box to complete your choice.
(Type an ordered pair. Use a comma to separate answers as needed.)
A. The second-derivative test for local extrema fails at (x,y) = .
B. The second-derivative test for local extrema does not fail for any of the critical points.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(Use a comma to separate answers as needed.)
A. The local maximum/maxima is/are
B. The local minimum/minima is/are
C. Since the second-derivative test for local extrema is inconclusive for some critical points, there may or may not
be local extrema.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 3 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt