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For x in [-6, 6], let f(x) = (x + 1)(x + 2)(x + 3)(x + 4) + 5. If the range of f is [a, b] with a, b natural numbers, find a + b.

1. 5049
2. 5045
3. 366
4. 5054

Correct answer: 5049

Solution

Writing f as a perfect square plus a constant shows its minimum; evaluating at the endpoints of the allowed t-range gives its maximum.

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