In calculus, Bolzano's Intermediate Value Theorem guarantees that a continuous function on has at least one root in under which condition?

Answer and explanation

Correct answer: B.

  1. Step 1: Bolzano's theorem requires continuity and that the function takes values with opposite signs at the endpoints. Step 2. Opposite signs mean and have product strictly less than zero: . **Answer: . Why not the others:** Product means identical signs; implies monotonicity; is Rolle's condition.

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