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) = x³, x $\in$ [-2, 2]

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Answer

It is given that f(x) = x³, x $\in$ [-2, 2]
$\Rightarrow$ f'(x) = 3x²
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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