JEE Math Practice Question

If a function f(x) defined by $$f\left( x \right) = \left\{ {\begin{matrix} {a{e^x} + b{e^{ - x}},} & { - 1 \le x < 1} \\ {c{x^2},} & {1 \le x \le 3} \\ {a{x^2} + 2cx,} & {3 < x \le 4} \\ \end{matrix} } \right.$$ be continuous for some $$a$$, b, c $$ \in $$ R and f'(0) + f'(2) = e, then the value of of $$a$$ is :

1. A.$${e \over {{e^2} - 3e - 13}}$$
2. B.$${1 \over {{e^2} - 3e + 13}}$$
3. C.$${e \over {{e^2} - 3e + 13}}$$
4. D.$${e \over {{e^2} + 3e + 13}}$$