`f(x) = x^2 - x - 2` Find the two x-intercepts of the function `f` and show that `f'(x) = 0` at some point between the two x-intercepts.

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Chapter 3, 3.2 - Problem 5 - 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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The x-intercepts are roots of f(x)=0. There are only two of those: -1 and 2.

The point between them where f'(x)=0 exists by Rolle's Theorem and we can find it:

f'(x)=2x-1, it is zero only at x=1/2.

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