This is not necessarily true. Let A = (-3, 0) and B = (-5, 0). Then C = (0, 15), but (inf A) * (inf B) = 15.
Edit: Since the problem is about calculus, it should go into the Calculus forum.
Hey can anyone help me prove this problem?
Let A and B be a subsets of R and bounded above.
Let InfA=a and InfB=b.
Let C= {xy ; x belongs to A, and y belongs to B}
Prove that InfC=ab