The absolute maximum value of the function f(x) = x³ − 3x² + 1 on the interval [−1, 3] is:
The absolute maximum value of the function f(x) = x³ − 3x² + 1 on the interval [−1, 3] is:
- A. 1
- B. −1
- C. −3
- D. 3
Answer: A) 1
Explanation: f'(x) = 3x² − 6x = 3x(x − 2). Critical points: x = 0, 2. f(−1) = −1 − 3 + 1 = −3. f(0) = 1. f(2) = 8 − 12 + 1 = −3. f(3) = 27 − 27 + 1 = 1. Maximum is 1.
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