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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The function $f(x)=x^3+3 x$ is increasing in interval
  • A
    $(-\infty, 0)$
  • B
    $(0, \infty)$
  • C
    $R$
  • D
    $(0,1)$
✓

Answer

f(x)=$x^3+3 x$
For increasing, we must have $f^{\prime}(x)>0$
$
\therefore f^{\prime}(x)=3 x^2+3>0 \Rightarrow 3\left(x^2+1\right)>0
$
$\Rightarrow x^2+1>0$, which is true $\forall x \in R$.

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