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Consider the function f(x) = x² − x − 2. The maximum value of f(x) in the closed interval [−4, 4] is

1. 18
2. 10
3. −2.25
4. indeterminate

Correct answer: 18

Solution

The function f(x) = x² − x − 2 is a quadratic function that opens upwards, meaning it has a minimum point. To find the maximum value on the closed interval [-4, 4], we evaluate the function at the endpoints, and since f(4) = 18 is greater than f(-4) = 10, the maximum value is 18.

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