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Let f : R → R be defined as, f(x) = { −55x, if x < −5 { 2x³ − 3x² − 120x, if −5 ≤ x ≤ 4 { 2x³ − 3x² − 36x − 336, if x > 4 Let A = { x ∈ R : f is increasing }. Then A is equal to :

1. (−∞, −5) ∪ (4, ∞)
2. (−5, ∞)
3. (−∞, −5) ∪ (−5, 4) ∪ (4, ∞)
4. (−5, 0)

Correct answer: (−5, 0)

Solution

The function f is increasing in the interval (-5, 0) because its derivative is positive in this range, indicating that the function's slope is upward. In other intervals, either the derivative is negative or the function is not defined, which means it does not consistently increase.

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