Question: . Suppose f is a real continuous function on [0, +), which is differentiable in (0, +) and such that f(0) = 0 and f'(0)

. Suppose f is a real continuous function on [0, +), which is differentiable in (0, +) and such that f(0) = 0 and f'(0) is monotonically increasing on (0, +). Consider the function g(x) = f(x)/x which is defined on (0, +). Prove that g(x) is monotonically increasing on (0, +).

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