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AP Calculus BC · Question of the Day

AP Calculus BC Question of the Day

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Friday, November 6, 2026

A continuous function rr on [−4,2][-4,2] has critical points x=−3,−1x=-3,-1 with r(−4)=−2,r(−3)=1,r(−1)=−3,r(2)=0r(-4)=-2,r(-3)=1,r(-1)=-3,r(2)=0. Where is the absolute minimum?

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Question of the Day

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A continuous function rr on [−4,2][-4,2] has critical points x=−3,−1x=-3,-1 with r(−4)=−2,r(−3)=1,r(−1)=−3,r(2)=0r(-4)=-2,r(-3)=1,r(-1)=-3,r(2)=0. Where is the absolute minimum?

  1. At x=−3x=-3
  2. At x=2x=2
  3. At x=−4x=-4
  4. At x=−1x=-1 (correct answer)
  5. At x=−4x=-4 and x=−1x=-1 (a tie)

Explanation: The Candidates Test is a method to find absolute extrema of a continuous function on a closed interval by evaluating the function at critical points and endpoints. Critical points are key as they may mark the lowest points where the function dips. Endpoints must be assessed because the minimum could occur at the interval's edge. This systematic comparison identifies the true absolute minimum. One tempting option is x=-3 with r(-3)=1, but it fails as it's higher than r(-1)=-3, showing a critical point oversight. Always list and evaluate the function at: both endpoints and all critical points within the interval.