Consider the polynomial $f(x) = x^{3} – 6x^{2} + 11x – 6$ on the domain $S$ given by $1 \leq x \leq 3.$ The first and second derivatives are $f’(x)$ and $f’’(x).$

Consider the following statements:

- The given polynomial is zero at the boundary points $x = 1$ and $x = 3.$
- There exists one local maxima of $f(x)$ within the domain $S.$
- The second derivative $f’’(x) > 0$ throughout the domain $S.$
- There exists one local minima of $f(x)$ within the domain $S.$

The correct option is:

- Only statements $\text{I, II}$ and $\text{III}$ are correct.
- Only statements $\text{I, II}$ and $\text{IV}$ are correct.
- Only statements $\text{I}$ and $\text{IV}$ are correct.
- Only statements $\text{II}$ and $\text{IV}$ are correct.