Question

The absolute minimum and maximum values of $f\left(x\right)=x^3,x\in [-2,2]$ are respectively.

• A. $6,0$
• B. $6,2$
• C. $-8,8$
• D. $8,0$

Answer 1

The correct option is C $-8,8$

Differentiate $f\left(x\right)=x^3$ with respect to $x$.

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

Put $f^{\prime }\left(x\right)=0$, then,

$3x^2=0$

$x=0$

Calculate the maximum and minimum values of the given function by substituting the value of $x$ and the end points of the given interval in the given function.

$f\left(0\right)={\left(0\right)}^3$

$=0$

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

$=-8$

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

$=8$

It can be observed that the minimum value is $-8$ and the maximum value is $8$.