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Question: find values of a at which an implicit function has a max,min,saddle point at y=0

Question:find values of a at which an implicit function has a max,min,saddle point at y=0

GPY 80 Maple
optimization calculus homework
March 04 2015
0

I've got

f(x,y)= a.exp(1+xy) +( a^2 )*sin(x)+1

for which I've shown that there exists an implicit function x=g(y). ( df/dx <>0)

and df/dx = a*exp(1+xy) +( a^2 )*cosx now in the neighborhood of P=(0,0) for the implicit function to exist I'd need a*exp(1+xy)*y <>0 but at P, wouldn't this be 0?

Given, g(y)=x, how do I find the max,min,saddle points?
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