Find the local extrema of the following function. f(x,y)=x -12xy +96y? ..... 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.) O A. The second-derivative test for local extrema does not fail for any of the critical points. O B. The second-derivative test for local extrema 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.) O A. The local minimum/minima is/are O B. The local maximum/maxima is/are O C. Since the second-derivative test for local extrema is inconclusive for some critical points, there may or may not be local extrema