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Let $f$ be a polynomial of degree $n \geq 3$ all of whose roots are non-positive real numbers. Suppose that $f(1)=1$. What is the maximum possible value of $f^{\prime}(1)?$

1. $1$
2. $n$
3. $n+1$
4. $\frac{n(n+1)}{2}$
5. $f^{\prime}(1)$ can be arbitrarily large given only the constraints in the question