Let $f: R \rightarrow R$ be a function defined by $f(x) = (x - 3)^{n_{1}}(x - 5)^{n_{2}}$,where $n_{1}, n_{2} \in N$. Which of the following is $\text{NOT}$ true?

• A
  For $n_{1} = 3, n_{2} = 4$,there exists $\alpha \in (3, 5)$ where $f$ attains a local maximum.
• B
  For $n_{1} = 4, n_{2} = 3$,there exists $\alpha \in (3, 5)$ where $f$ attains a local minimum.
• C
  For $n_{1} = 3, n_{2} = 5$,there exists $\alpha \in (3, 5)$ where $f$ attains a local maximum.
• D
  For $n_{1} = 4, n_{2} = 6$,there exists $\alpha \in (3, 5)$ where $f$ attains a local maximum.