The function f(x) = x³ - 3x + 3 is defined on the closed interval [-2, 2]. What is the absolute maximum value of the function?

Model Answer & Options

Source: Extra Practice

1

5

3

4

Explanation

First, find critical points: f'(x) = 3x² - 3 = 0 => x² = 1 => x = 1, -1. Evaluate f(x) at critical points and endpoints: f(-2) = (-8) - 3(-2) + 3 = 1; f(-1) = (-1) - 3(-1) + 3 = 5; f(1) = 1 - 3(1) + 3 = 1; f(2) = 8 - 3(2) + 3 = 5. The maximum value reached in this set is 5.

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