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$f (x) = {\begin{matrix} 2 - | x^{2} + 5 x + 6 | & x \neq - 2 \\ a^{2} + 1 & x = - 2 \end{matrix}$
Then the range of a so that $f (x)$ has a maxima at $x = - 2$

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$a < 1$

$a > 1$

$| a | < 1$

$| a | \geq 1$

answer is A.

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$a^{2} + 1 \geq 2 \Rightarrow | a | \geq 1$

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