Find the absolute maximum value and the absolute minimum value of… - Vidyadip

Question

Find the absolute maximum value and the absolute minimum value of the function:
$f(x) = x^3, x \in [-2, 2]$

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Answer

It is given that $ f(x) = x^3, x \in [-2, 2]$
$\Rightarrow f'(x) = 3x^2$
Now $, f'(x) = 0$
$\Rightarrow x = 0$
Further, we evaluate the value of f at critical point $x = 0$ and at end points of the interval $[-2, 2]$.
$f(0) = 0$
$f(-2) = (-2)^3 = -8$
$f(2) = (2)^3 = 8$
Therefore, the absolute maximum value of f on $[-2, 2]$ is $8$ occurring at $x = 2$
And, the absolute minimum value of f on $[-2, 2] $ is $-8$ occurring at $x = -2$

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