For which of the following function, Rolle's hypothesis is not satisfied?

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

For which of the following function, Rolle's hypothesis is not satisfied? (a)

f(x) = x^{\frac{4}{3}}, x \in [-1, 1]

(b)

k(x) = |x| + |x-2|, x \in [0, 2]

(c)

h(x) = x + \frac{1}{x}, x \in [\frac{1}{5}, 5]

(d)

g(x) = \begin{cases} \cos(\frac{1}{x}), & x \in [-1, 0] \cup (0, 1) \\ 0, & x = 0 \end{cases}