If a function f(x) defined by f(x) = \ a eˣ + b e⁻ˣ, - 1 ≤ x < 1 c x², 1 ≤ x ≤ 3 a x² + 2cx, 3 < x ≤ 4. be continuous for some a, b, c R and f'(0) + f'(2) = e, then the value of of a is:

Limit, Continuity and Differentiability: JEE Main 2020 Mathematics question

JEE Main 2020 · 2 Sep, Morning shift · Q4139

JEE Main 20202 Sep, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

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 :