`f(x) = |x| - 1, [-1,1]` Use a graphing utility to graph the function on the closed interval `[a,b]`. Determine whether Rolle's Theorem can be applied to `f` on the interval and, if so, find...

`f(x) = |x| - 1, [-1,1]` Use a graphing utility to graph the function on the closed interval `[a,b]`. Determine whether Rolle's Theorem can be applied to `f` on the interval and, if so, find all values of `c` in the open interval `(a,b)` such that `f'(c) = 0`.

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Textbook Question

Chapter 3, 3.2 - Problem 23 - Calculus of a Single Variable (10th Edition, Ron Larson).
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tiburtius | High School Teacher | (Level 2) Educator

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Rolle's theorem cannot be applied because the function is not differentiable over the whole interval `(-1,1).`  More specifically the function is not differentiable at zero. Graph of the function is shown on the image below. It is obvious that the function is not differentiable at zero because the graph shows spike at `x=0.`           

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