A function f (x) is defined as \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {{e^x},}&{x < 1}\\ {\ln x + a{x^2}+bx,}&{x \ge 1} \end{array}} \right.\), where x ϵ R. Which one of the following statements is TRUE?
1
f(x) is NOT differentiable at x = 1 for any values of a and b
2
f(x) is differentiable at x = 1 for the unique value of a and b.
3
f(x) is differentiable at x = 1 for all values of a and b such that a + b = e
4
f(x) is differentiable at x = 1 for all values of a and b.