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Assume that the function $f:[0,?)?R$ is continuous and that $f(0)=0$. In addition, assume that $f$ is differentiable on $(0,?)$ and that $f_{?}$ is strictly increasing, i.e., for all $s,t?(0,?)$ we have $s<t?f_{?}(s)<f_{?}(t).$ Use the Mean Value Theorem to prove that the function $g:(0,?)?R$ defined by $g(x)=f(x)/x$ is strictly increasing.

Given that the function f:[0,?)?R i

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