Mean Value Theorem

Question

Suppose f(x) = 1/x. Then Show that the Mean Value Theorem is not satisfied on (-1,1).

Answer 1

For the mean value theorem to be satisfied, it must be continuous on [-1,1].

It is discontinuous at x = 0.

lim x→0^- 1/x = -∞

lim x→0⁺ 1/x = +∞

also f '(c) = -1/c² = (1-(-1))/(1-(-1)) = 1 --> c = √-1 which is not ∈R