`f(x) = |1/x|, [-1,1]` Explain why Rolle’s Theorem does not apply to the function even though there exist `a` and `b` such that `f(a) = f(b)`.

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Chapter 3, 3.2 - Problem 1 - Calculus of a Single Variable (10th Edition, Ron Larson).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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Rolle's Theorem requires the function to be continuous on the closed interval [a, b]. But this function isn't. The problem point is x=0. Aclually, f(x) isn't even defined at x=0, and because `lim_(x-gt0)[f(x)] = +oo,` there is no possible value for f(0) to make it continuous.

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