Question

The function $f\left(x\right)=x^3-3x$ is

• A. increasing in $(-\infty ,-1)U(1,\infty )$ and decreasing in $(-1,1)$
• B. decreasing in $(-\infty ,-1)U(1,\infty )$ and increasing in $(-1,1)$
• C. increasing in $(0,\infty )$ and decreasing in $(-\infty ,0)$
• D. decreasing in $(0,\infty )$ and increasing in $(-\infty ,0)$

Answer 1

The correct option is A increasing in $(-\infty ,-1)U(1,\infty )$ and decreasing in $(-1,1)$

$f\left(x\right)=x^3-3x$
$f^{\prime }\left(x\right)=3x^2-3$
$f^{\prime }\left(x\right)=0\Rightarrow x=-1,1$
Hence,$f^{\prime }\left(x\right)>0$ in $(-\infty ,-1)\cup (1,\infty )$ and $f^{\prime }\left(x\right)<0$ in $(-1,1)$
Hence,$f\left(x\right)$ is increasing in $(-\infty ,-1)\cup (1,\infty )$ and decreasing in $(-1,1)$.