4) Convex functions are important in constrained optimization. a) For a real valued function f(x,y) defined on all of R2, what property must f have in order to be a convex function? Use x and y in your definition, and you will also need to use the phrase "for all ..." or the phrase "there exists a ..." b) Is it true that when f(x,y) is convex and g(x,y) is convex then the function f+g is convex? Explain. c) Is it true that when f(x,y) is convex and g(x,y) is convex then the function f*g is convex? Explain. d) Is it true that when f(x,y) is convex and g(x,y) is convex then the function max(f,g) is convex? Explain