Explain why Lagrange’s mean value theorem is not applicable to the f

1.	Explain why Lagrange’s mean value theorem is not applicable to the following functions in the respective intervals:(i) f(x) = (x + 1)/x, x ∈ [-1,2](ii) f(x) = \|3x + 1\|, x ∈ [-1,3]
Answer» (i) f(x) = (x + 1)/x The function is not continuous at x = 0. So Lagrange’s mean value theorem is not applicable in the given interval. (ii) f(x) = \|3x + 1\|, x ∈ [-1, 3] The function is not differentiable at x = -1/3. So Lagrange’s mean value theorem is not applicable in the given interval.

Explain why Lagrange’s mean value theorem is not applicable to the following functions in the respective intervals:(i) f(x) = (x + 1)/x, x ∈ [-1,2](ii) f(x) = |3x + 1|, x ∈ [-1,3]

Answer»

(i) f(x) = (x + 1)/x

The function is not continuous at x = 0. So Lagrange’s mean value theorem is not applicable in the given interval.

(ii) f(x) = |3x + 1|, x ∈ [-1, 3]

The function is not differentiable at x = -1/3. So Lagrange’s mean value theorem is not applicable in the given interval.