A fifth-degree polynomial in $x$ is defined for $x>0$. All coefficients of the polynomial are positive. The first derivative of the polynomial is obtained numerically at a point by using the first-order forward as well as the first-order backward difference methods. Identical step lengths are used for both the methods.
Following statements are made.
- Forward difference method underestimates the true derivative.
- Backward difference method overestimates the true derivative.
Which one of the following options is CORRECT?
- Both statements $\text{(I)}$ and $\text{(II)}$ are FALSE.
- Both statements $\text{(I)}$ and $\text{(II)}$ are TRUE.
- Statement $\text{(I)}$ is TRUE and statement $\text{(II)}$ is FALSE.
- Statement $\text{(I)}$ is FALSE and statement $\text{(II)}$ is TRUE.
