Saddle Points and Inflection Points
Saddle Points and Inflection Points
Theorem: Let be a function with continuous second partial derivatives in a open set in the plane and let be a saddle point in . Then there exists a continuous function with for which the projection on the plane of the intersection of the surface and the cylindrical surface has a inflection point at .
f
U
(a,b)
U
y=g(x)
g(a)=b
xz
z=f(x,y)
y=g(x)
x=a