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AP Calculus BC · Question of the Day

AP Calculus BC Question of the Day

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Friday, August 7, 2026

If f′(x)=−(x+2)(x−4)f'(x)=-(x+2)(x-4), on which interval(s) is ff increasing?

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Question of the Day

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If f′(x)=−(x+2)(x−4)f'(x)=-(x+2)(x-4), on which interval(s) is ff increasing?

  1. (−∞,−2)∪(4,∞)(-\infty,-2)\cup(4,\infty)
  2. (−2,4)(-2,4) (correct answer)
  3. (−∞,4)(-\infty,4)
  4. (−2,∞)(-2,\infty)
  5. (−∞,−2)(-\infty,-2)

Explanation: Determining the intervals on which a function is increasing or decreasing is a key skill in AP Calculus BC that relies on analyzing the first derivative. Given f'(x) = -(x+2)(x-4), roots at x=-2, x=4. The negative sign flips the product: (x+2)(x-4) >0 outside roots, so - of that <0 outside, >0 inside. Specifically, product positive on (-∞,-2)∪(4,∞), so f'<0 there; product negative on (-2,4), so f'>0 there. Thus increasing on (-2,4). A tempting distractor like A, (-∞,-2)∪(4,∞), fails because that's where f'<0, decreasing. Always create a sign chart for the derivative to systematically determine intervals of increase and decrease.