Find the interval where function f(x)=x^3-3 x is decreasing. - Vidyadip

Question

Find the interval where function $f(x)=x^3-3 x$ is decreasing.

✓

Answer

$
\begin{aligned}
f(x) & =x^3-3 x \\
f^{\prime}(x) & =3 x^2-3=3\left(x^2-1\right)
\end{aligned}
$
For decreasing $f^{\prime}(x) \leq 0$
$\begin{aligned} \Rightarrow & & 3\left(x^2-1\right) & \leq 0 \\ \Rightarrow & & x^2 & \leq 1 \\ \Rightarrow & & -1 & < x<1 \\ \Rightarrow & & x & \in(-1,1)\end{aligned}$

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