Let f and g be twice-differentiable real-valued functioned defined on R. If f'(x) > g'(x) for all x > 0, which of the following inequalities must be true for all x > 0 ?
(A) f(x) > g(x)
(B) f''(x) > g''(x)
(C) f(x) - f(0) > g(x) - g(0)
(D) f'(x) - f'(0) > g'(x) - g'(0)
(E) f''(x) - f''(0) > g''(x) - g''(0)

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This is an interesting question, have you gotten anywhere with it?

I'd say C-E are ruled out, since you can't make any assumptions about f(0) or g(0)

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