CONVEX FUNCTIONS & THEIR CHARACTERIZATIONS 5 Some Examples of Convex Functions 1. flx) = Sx + 7 2. f(x) = Ixl 3. flx) =x2 _ 2x 4. f(x) =-xz, x z 0 5. f(x,y) = 2x2 +y2 2xy Exercise: By sketching the graphs of the functions in the examples above, confirm that they are indeed convex (according to the definition):