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Limits Continuity and Differentiability question

2020 · 2 Sep · Shift 1 · Q23

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JEE Main
Mathematics
Limits Continuity and Differentiability
2020 · 2 Sep · Shift 1 · Q23

Limits Continuity and Differentiability question

2020 · 2 Sep · Shift 1 · Q23

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

If a function f(x) defined by

f\left( x \right) = \left\{ {\begin{matrix} {a{e^x} + b{e^{ - x}},} & { - 1 \le x \lt 1} \\ {c{x^2},} & {1 \le x \le 3} \\ {a{x^2} + 2cx,} & {3 \lt 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 :

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

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