Unformatted text preview: x 2 y 2 z 2 )-x-y-z (e) f ( x, y, z ) = x 2 + y 2 + z 2-cos( x 2 + y 2 + z 2 ) 3. (532 only) Suppose that f : R n → R is a function with continuous second-order partial derivatives whose Hessian is positive deﬁnite at all points in R n . (a) Show that f has at most one critical point. (b) Show, by example, that f may have no critical points. (c) Show that if x * is a critical point of f , then x * is a strict global minimizer of f . (d) Show that if ∇ f ( x (1) ) = ∇ f ( x (2) ), then x (1) = x (2) ....
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- Spring '12
- Critical Point, hessian matrix