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