Question

If $f$ be a function defined as $f\left(x\right)=x^3-3x,-1\le x\le$ 3 then the range of $f$ is

• A. $[0,24]$
• B. $[-2,2]$
• C. $[-2,18]$
• D. none of these

Answer 1

The correct option is B $[-2,2]$

Domain for the following function is $[-1,3]$

Therefore

$f(-1)=-1+3$ $=2$

$f\left(3\right)=27-9$

$=18$

$f^{\prime }\left(x\right)$ $=3x^2-3$

Equating it with zero, we will get the minima

$3x^2-3=0$

$x=\pm 1$

$f(-1)=2$ and $f\left(1\right)=1-3$ $=-2$

Hence the range of $f\left(x\right)$ for $x\in [-1,3]$ is $[-2,2]$

Hence, option 'B' is correct.