Let and be concave functions over a convex set . Let , + 0, 0. Define the function + over to be ( + )() = () + (). Prove that the function + is a concave function over . (6) General case: If 1, 2, ... , are concave functions over the convex set and = ( , , ... , ) then 1 + 2 + is a concave function over the 12 + 1 2 set . Don't need to prove. Here 2, 3, just means a second function, third function, etc, not the square of a function, cube, etc. Similar results apply to convex functions