`f(x) = x - tan(pix), [(-1/4),(1/4)]` 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,...

`f(x) = x - tan(pix), [(-1/4),(1/4)]` 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 25 - 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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NO, Rolle's Theorem isn't applicable because the function doesn't has equal values at the endpoints:

f(1/4) = 1/4 - tan(pi/4) = 1/4 - 1 = -3/4

while

f(-1/4) = -1/4 - tan(-pi/4) = -1/4 + 1 = 3/4.

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