If a function f(x) defined by

$f(x) = \begin{cases}ae^x+be^{-x}&,&-1\leq x<1\\cx^2&,&1\leq x\leq3\\ ax^2+2cx&,&3<x\leq4\end{cases}$

be continuous for some a, b, c $\in$ R and f'(0) + f'(2) = e, then the value of a is :

(1) $1\over e^2-3e+13$

(2) $e\over e^2-3e+13$

(3) $e\over e^2-3e-13$

(4) $e\over e^2+3e+13$

$f(x) = \begin{cases}ae^x+be^{-x}&,&-1\leq x<1\\cx^2&,&1\leq x\leq3\\ ax^2+2cx&,&3<x\leq4\end{cases}$

be continuous for some a, b, c $\in$ R and f'(0) + f'(2) = e, then the value of a is :

(1) $1\over e^2-3e+13$

(2) $e\over e^2-3e+13$

(3) $e\over e^2-3e-13$

(4) $e\over e^2+3e+13$