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## Homework Statement

this is from ch9 (functions of several variables)of baby rudin

a,b real b>a>0 define a mapping f=(f

_{1},f

_{2}),f

_{3}) of R2 into R3 by

f

_{1}(s,t)=(b+acos(s))cos(t)

f

_{2}(s,t)=(b+acos(s))sin(t)

f

_{2}(s,t)=asin(s)

I showed that there are exactly 4 points p in K=image(f) such that

gradf

_{1}(f

^{-1}(p))=0

I am having trouble finding which of these points are local min, max, and saddle points.

## 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.