MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Let f(x)=∣x−2∣ on the interval [0,4]. Which statement correctly describes the applicability of the Mean Value Theorem on this interval?
(a) The theorem applies because f is continuous on [0,4]; differentiability is not required.
(b) The theorem does not apply because f fails to be differentiable at the endpoints x=0 and x=4.
(c) The theorem does not apply because f is not differentiable at x=2, an interior point of the interval.
(d) The theorem applies if the point x=2 is removed from the interval since the theorem is concerned only with the open interval.