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Let f be differentiable for all x. If f(1) = -2 and f'(x) ≥ 2 for x ∈ [1, 6], then
- f(6) ≥ 8
- f(6) < 8
- f(6) < 5
- f(6) = 5
Correct answer: f(6) ≥ 8
Solution
Since the derivative f'(x) is always greater than or equal to 2 on the interval [1, 6], this indicates that the function f is increasing at a rate of at least 2 units for every unit increase in x. Starting from f(1) = -2, after 5 units of increase (from x=1 to x=6), the minimum value of f(6) can be calculated as f(1) + 5 * 2 = -2 + 10 = 8, thus f(6) must be at least 8.
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