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Let f(x) = x³ + 15x² - 33x - 36 be a real-valued function. Which of the following statements is/are TRUE?

1. f(x) does not have a local maximum.
2. f(x) has a local maximum.
3. f(x) does not have a local minimum.
4. f(x) has a local minimum.

Correct answer: f(x) has a local maximum.

Solution

The function f(x) has a local maximum because its first derivative changes from positive to negative at a certain point, indicating that the function reaches a peak there.

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