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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The interval on which the function $f(x)=2 x^3+9 x^2+12 x-1$ is decreasing is
  • A
    $[-1, \infty)$
  • ✓
    $[-2,-1]$
  • C
    $(-\infty,-2]$
  • D
    $[-1,1]$
✓

Answer

Correct option: B.
$[-2,-1]$
$f(x)=2 x^3+9 x^2+12 x-1$
$f^{\prime}(x)=6 x^2+18 x+12=6\left(x^2+3 x+2\right)=6(x+2)(x+1)$
For decreasing function, $f^{\prime}(x) \leq 0$
$\therefore 6(x+2)(x+1) \leq 0$
$\Rightarrow \quad(x+2)(x+1) \leq 0 \Rightarrow-2 \leq x \leq-1$

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