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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
Function $f(x)=x^3-27 x+5$ is monotonically increasing when :
  • A
    $\text{x} < -3$
  • ✓
    $|\text{x}| > 3$
  • C
    $\text{x}\leq-3$
  • D
    $|\text{x}|\geq3$
✓

Answer

Correct option: B.
$|\text{x}| > 3$
$f(x)=3 x^2-27 x$
$\Rightarrow f^{\prime}(x)=x^3-27 x+5$
$\Rightarrow f^{\prime}(x)=3\left(x^2-9\right)$
Function is increasing,
$3\big(\text{x}^2-9\big)\geq0$
$\Rightarrow\text{x}^2\geq9$
$\Rightarrow|\text{x}|\geq3$

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