Q1-xxvi

There must be a root of $f(x)$ between $x_i$ and $x_{i+1}$

There need not be a root of $f(x)$ between $x_{i}$ and $x_{i+1}$

There fourth derivative of $f(x)$ with respect to $x$ vanishes at $x_{i}$

The fourth derivative of $f(x)$ with respect to $x$ vanishes at $x_{i+1}$