17 Consider the problem max z  f (x)

s.t. a  x  b a Suppose f (x) is a convex function that has derivatives for all values of x. Show that x  a or x  b must be optimal for the NLP. (Draw a picture.)

b Suppose f(x) is a convex function for which f (x) may not exist. Show that x  a or x  b must be optimal for the NLP. (Use the definition of a convex function.)