An interesting function

Calculus Level 4

\(f(x)\) is a non-negative function defined for \(x\geq1\) such that the inequality \(f '(x)\leq m \cdot f(x)\) holds everywhere in the domain for some positive real number \(m\). If \(f(1)=0\) then find the value of \(f(e)+f(e^2)\).

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