Question

The minimum value of the function $f\left(x\right)=x^3-3x^2-24x+100$ in the interval $[-3,3]$ is

• A. $20$
• B. $28$
• C. $16$
• D. $32$

Answer 1

The correct option is B $28$

$f\left(x\right)=x^3-3x^2-24x+100,xϵ[-3,3]$
$f^{\prime }\left(x\right)=3x^2-6x-24=0$
$x^2-2x-8=0$
$x=4,-2$
Since $4\text{/}ϵ[-3,3]$, $x=-2$
Value of $f\left(x\right)$ at critical and boundaries:

$x$	$-3$	$-2$	$3$
$f\left(x\right)$	$118$	$128$	$28$

$\therefore$ Minimum value of $f\left(x\right)=28$.