Question

Find the absolute maximum and absolute minimum value of the following function :

$f\left(x\right)=x^3,x\in [-2,2]$

Answer 1

$f\left(x\right)=x^3$

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

Now, $f^{\prime }\left(x\right)=0⟹x=0$

Then, we evaluate the value of f at critical point $x=0$ and at the end points of the interval [-2,2].

$f\left(0\right)=0$

$f(-2)=-8$

$f\left(2\right)=8$

Hence, absolute maximum value of f on [-2,2] is 8 occurring at x = 2 and absolute minimum value of f on [-2,2] is -8 occurring at x = -2.