Question: Suppose that f(x) > 0 and g(x) > 0 for all x. What simple additional conditions (if any) are needed to guarantee that (a) f(x)

Suppose that f"(x) > 0 and g"(x) > 0 for all x. What simple additional conditions (if any) are needed to guarantee that
(a) f(x) + g(x) is concave up for all x;
(b) f(x) ∙ g(x) is concave up for all x;
(c) f(g(x)) is concave up for all x?

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