`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`.

Expert Answers
tiburtius eNotes educator| Certified Educator

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.`           

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)