You are given the function $C(n)=50\mathrm{.}5n\frac{4\mathrm{.}5}{n}.$ Determine which of the following conclusions would be the correct result of the second derivative test for the critical point at $n=3.$

$C(3)$ is a minimum because $C^{\text{'}}(3)=0$ and $C^{\text{'}\text{'}}(3)=0$

$C(3)$ is a minimum because $C^{\text{'}}(3)=0$ and $C^{\text{'}\text{'}}(3)<mn>0</mn>$

$C(3)$ is a minimum because $C^{\text{'}}(3)=0$ and $C^{\text{'}\text{'}}(3)>0$

$C(3)$ is a maximum because $C^{\text{'}}(3)=0$ and $C^{\text{'}\text{'}}(3)<mn>0</mn>$

$C(3)$ is a maximum because $C^{\text{'}}(3)=0$ and $C^{\text{'}\text{'}}(3)>0$