1. The problem statement, all variables and given/known data this is from ch9 (functions of several variables)of baby rudin a,b real b>a>0 define a mapping f=(f1,f2),f3) of R2 into R3 by f1(s,t)=(b+acos(s))cos(t) f2(s,t)=(b+acos(s))sin(t) f2(s,t)=asin(s) I showed that there are exactly 4 points p in K=image(f) such that gradf1(f-1(p))=0 I am having trouble finding which of these points are local min, max, and saddle points. 3. The attempt at a solution The points in question correspond to the touple (s,t) when s=(pi)k and t=(pi)j k,j integers. the points being +/-b +/-a Okay great, I do not have any developed criteria for the second derivative test, I have no Hessin matrix to work with. I can develop that in my problem, but that seems rather complicated, I have been trying for a while now, and am having trouble.