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6. Application of derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
$f(x) = \left\{ \begin{array}{l}
2 - \left| {{x^2} + 5x + 6} \right|,\,\,\,x \ne  - 2\\
{a^2} + 1,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x =  - 2
\end{array} \right.$ . Then the range of $a$ , so that $f(x)$ has maximum at $x = -2$, is
  • ✓
    $\left| a \right| \ge 1$
  • B
    $\left| a \right| < 1$
  • C
    $a > 1$
  • D
    $a < 1$
✓

Answer

Correct option: A.
$\left| a \right| \ge 1$
a
$f(x)$ will have maxima at $x=-2$ only if $a^{2}+1 \geq 2$ or

or $|\mathrm{a}| \geq 1.$

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