Question

Find the local extrema of the following function. f(x,y) = x^3 - 3xy^2 + 6y^2 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.) A. The function has (a) local maximum/maxima at (x,y) = B. The function has (a) local minimum/minima at (x,y) = C. There is/are (a) saddle point(s) at (x,y) = Does the second derivative test 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 does not fail for any of the critical points. B. The second derivative test fails at (x,y) = 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 minimum/minima is/are B. The local maximum/maxima is/are C. The function has no minima or maxima

          Find the local extrema of the following function.
f(x,y) = x^3 - 3xy^2 + 6y^2
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.)
A. The function has (a) local maximum/maxima at (x,y) = 
B. The function has (a) local minimum/minima at (x,y) = 
C. There is/are (a) saddle point(s) at (x,y) = 
Does the second derivative test 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 does not fail for any of the critical points.
B. The second derivative test fails at (x,y) = 
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 minimum/minima is/are 
B. The local maximum/maxima is/are 
C. The function has no minima or maxima

Find the local extrema of the following function.
f(x,y) = x^3 - 3xy^2 + 6y^2
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.)
A. The function has (a) local maximum/maxima at (x,y) =
B. The function has (a) local minimum/minima at (x,y) =
C. There is/are (a) saddle point(s) at (x,y) =
Does the second derivative test 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 does not fail for any of the critical points.
B. The second derivative test fails at (x,y) =
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 minimum/minima is/are
B. The local maximum/maxima is/are
C. The function has no minima or maxima

Added by Brandi O.

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