A function f(x) is defined as
\[{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {{{\text{e}}^x}}&{{\text{x}} < 1} \\ {\ln {\text{x}} + {\text{a}}{{\text{x}}^2} + {\text{bx}},}&{{\text{x}} \geqslant 1} \end{array}} \right.\]
where x\[ \in \] R which one of the following statements is TRUE?

A. f(x) is NOT differentiable at x = 1 for any values of a and b

B. f(x) is differentiable at x = 1 for the unique values of a and b

C. f(x) is differentiable at x = 1 for all the values of a and b such that a + b = e

D. f(x) is differentiable at x = 1 for all values of a and b

Answer: Option A