A function $f(x)$ is defined as
$f(x)= \begin{cases} e^{x}, & x < 1 \\ \text{In } x+ax^{2}+bx, & x\geq 1 \end{cases}$, where $x \in \mathbb{R}$
Which one of the following statement is TRUE?
- $f(x)$ is NOT differentiable at $x=1$ for any values of $a$ and $b$.
- $f(x)$ is differentiable at $x=1$ for the unique values of $a$ and $b$.
- $f(x)$ is differentiable at $x=1$ for all values of $a$ and $b$ such that $a+b=e$.
- $f(x)$ is differentiable at $x=1$ for all values of $a$ and $b$.