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