Given the following nonlinier system, find all of the critical points, construct the Jacobian matrix, and discuss the type and stability of the critical points. dx dt dy dt = 64-xy -=x-4y³ The critical point(s) occur(s) at. (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) Classify the critical points. Identify any unstable improper nodes. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The critical point(s) is/are (an) unstable improper node(s) because the eigenvalues of the linear system(s) that correspond(s) to the resulting almost linear system(s) are real, distinct, and positive. (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) OB. The system has no critical point that is an unstable improper node. Identify any asymptotically stable improper nodes. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The critical point(s) is/are (an) asymptotically stable improper node(s) because the eigenvalues of the linear system(s) that correspond(s) to the resulting almost linear system(s) are real, distinct, and negative. (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) OB. The system has no critical point that is an asymptotically stable improper node. Identify any unstable saddle points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The critical point(s) is/are (an) unstable saddle point(s) because the eigenvalues of the linear system(s) that correspond(s) to the resulting almost linear system(s) are real and have opposite signs. (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) OB. The system has no critical point that is an unstable saddle point. Identify any critical points that are unstable improper nodes, proper nodes, or spiral points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The critical point(s) is/are (an) unstable improper node(s), proper node(s), or spiral point(s) because the eigenvalues of the linear system(s) that correspond(s) to the resulting almost linear system(s) are real, equal, and positive. (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) OB. The system has no critical point that is an unstable improper node, proper node, or spiral point. Identify any critical points that are asymptotically stable improper nodes, proper nodes, or spiral points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The critical point(s) is/are (an) asymptotically stable improper node(s), proper node(s), or spiral point(s) because the eigenvalues of the linear system(s) that correspond(s) to the resulting almost linear system(s) are real, equal, and negative. (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) OB. The system has no critical point that is an asymptotically stable improper node, proper node, or spiral point. Identify any unstable spiral points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The critical point(s) is/are (an) unstable spiral point(s) because the eigenvalues of the linear system(s) that correspond(s) to the resulting almost linear system(s) are complex-valued with a positive real part. (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) OB. The system has no critical point that is an unstable spiral point. Identify any asymptotically stable spiral points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The critical point(s) is/are (an) asymptotically stable spiral point(s) because the eigenvalues of the linear system(s) that correspond(s) to the resulting almost linear system(s) are complex-valued with a negative real part. (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) OB. The system has no critical point that is an asymptotically stable spiral point. Identify any critical points that are centers or spiral points of indeterminate stability. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The critical point(s) is/are (a) center(s) or spiral point(s) of indeterminate stability because the eigenvalues of the linear system(s) that correspond(s) to the resulting almost linear system(s) are complex-valued and purely imaginary. (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) B. The system has no critical point that is a center or spiral point of indeterminate stability.