If a function f(x) defined byf(x)=⎧⎪⎨⎪⎩aex+be−x,−1≤x<1 – InterviewSolution

1.	If a function f(x) defined byf(x)=⎧⎪⎨⎪⎩aex+be−x,−1≤x<1cx2,1≤x≤3ax2+2cx3<x≤4be continuous for some a,b,c∈R and f′(0)+f′(2)=e, then the value of a is :
Answer» If a function $f (x)$ defined by $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} a e^{x} + b e^{- x}, & - 1 \leq x < 1 c x^{2}, & 1 \leq x \leq 3 a x^{2} + 2 c x & 3 < x \leq 4 \end{matrix}$ be continuous for some $a, b, c \in R$ and $f^{'} (0) + f^{'} (2) = e,$ then the value of $a$ is :

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