Question

Show that the Lagrange’s mean value theorem is not applicable to the function f(x) = 1/x on [–1, 1].

Answer 1

Given as f(x) = (1/x) on [-1,1]

It is clear, x ≠ 0

⇒ f (x) exists for all the values of x except 0

⇒ f (x) is the discontinuous at x = 0

So, f (x) is not continuous in [– 1, 1]

Thus, the Lagrange’s mean value theorem is not applicable for the function f(x) = 1/x on [-1, 1]