JEE PYQ: Continuity And Differentiability Question 12
Question 12 - 2020 (02 Sep Shift 1)
If a function $f(x)$ defined by
$$f(x) = \begin{cases} ae^x + be^{-x}, & -1 \leq x < 1 \ cx^2, & 1 \leq x \leq 3 \ ax^2 + 2cx, & 3 < x \leq 4 \end{cases}$$
be continuous for some $a, b, c \in \mathbb{R}$ and $f’(0) + f’(2) = e$, then the value of $a$ is:
(1) $\dfrac{1}{e^2 - 3e + 13}$
(2) $\dfrac{e}{e^2 - 3e - 13}$
(3) $\dfrac{e}{e^2 + 3e + 13}$
(4) $\dfrac{e}{e^2 - 3e + 13}$
BETA
