The function f(x)=x^3+3 x is increasing in interval - Vidyadip

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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