Question at position 6 The function f(x) = x2 - 6x + 8 is decreasing on(2, 4).(3, ∞).(-∞, 3).(-∞, 2) and (4, ∞).(-3, 3).

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Question at position 6 The function f(x) = x2 - 6x + 8 is decreasing on(2, 4).(3, ∞).(-∞, 3).(-∞, 2) and (4, ∞).(-3, 3).

BlackTom AI · Accepted Answer

We start by identifying the function and where it decreases. The function is f(x) = x^2 - 6x + 8, a parabola opening upward. Its derivative is f'(x) = 2x - 6, which is negative when x < 3 and positive when x > 3. Therefore, f is decreasing on the interval (-∞, 3) and increasing on (3, ∞). Option 1: (2, 4). This interval crosses x = 3; the function decreases on (−∞, 3) but increases on (3, ∞). Since (2,4) includes values to the right of 3, f is not decreasing on the entire interval (2,4). Hence this option is incorrect. Option 2: (3, ∞). On this interval, f is increasing (not decreasing), because for x > 3, f'(x) > 0. So this option is incorrect. Option 3: (−∞, 3). This matches the region where f'(x) < 0, i.e., where the function is decreasing. It is the correct description of the decreasing interval. Option 4: (−∞, 2). While f is decreasing on (−∞, 2) as a subset of (−∞, 3), this option omits the portion (2, 3) where the function also decreases. Since the statement asks for the interval on which the function is decreasing, picking only (−∞, 2) fails to capture the full decreasing region and is therefore not correct. Option 5: (−3, 3). This interval lies entirely within the decreasing region (since all x < 3 here). The function is indeed decreasing on (−3, 3), but the question asks for the interval over which it is decreasing in general, and (−∞, 3) is the maximal interval of decrease. Therefore this option is not the complete answer and is considered incorrect in this context. In summary, the only interval that correctly and maximally describes where f is decreasing is (−∞, 3).

Question at position 6 The function f(x) = x2 - 6x + 8 is decreasing on(2, 4).(3, ∞).(-∞, 3).(-∞, 2) and (4, ∞).(-3, 3).Single choice

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