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Unformatted text preview: . Give an example of a convex function g : R R such that ( g ( x )-3) 2 is not convex. 4. Let f : R n R be strictly convex, and suppose f ( x ) = f ( y ) = 0 for two points x and y in R n with x 6 = y . Show that there exists z R n such that f ( z ) < . 5. (532 only) Let f : R n R have continuous rst-order partial derivatives at all points in R n . Show that f is convex if and only if ( f ( x )- f ( y )) ( x-y ) 0 for all x, y in R n ....
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- Spring '12