Question

The minimum value of the function $f\left(x\right)=\frac{1}{3}x(x^2-3)$ in the interval $-100\le x\le 100$ occurs at $x=$

• A. -100

Answer 1

The correct option is A -100
$f\left(x\right)=\frac{1}{3}x(x^2-3)$
Its graph will be



$\frac{df}{dx}=3x^2-3=0$
So, local maxima $\&$ minima occurs at $x=1$ and $-1$ and gives $y=2/3$ and $-2/3.$
As it is in free fall below $x=-1.$ So minimum will occur at $x=-100.$

Or



So, from $x=-100tox=-1,$ function is an increasing function.
Hence, minimum value occurs at $x=-100.$