Let A be a 3*3 matrix with eigenvalues 1,-1 and 3.then

Find the critical points of the function f(x,y)=x^3+y^2-12x-6y+40 test each of these for maximum and minimum

Let A be a 3*3 matrix with eigenvalues 1,-1 and 3.then

Then? What are you supposed to do?

Find the characteristic polynomial? I don't know.

A 3 by 3 matrix will have a cubic as a charpoly.

({\lambda}+1)({\lambda}-1)({\lambda}-3)={\lambda}^{3}-3{\lambda}^{2}-{\lambda}+3

Do you have to find the eigenvectors? Let us know what you need to do. We are good, but not mindreaders.:D

Find the critical points of the function f(x,y)=x^3+y^2-12x-6y+40 test each of these for maximum and minimum

Assistance given in other post regarding same problem.