For the function f(x) = , c ∈ [1, 3], the value of c for mean value theorem is:

Question

Question

Answer 1

Concept:

Lagrange’s Mean Value Theorem:
If a function f is defined on the closed interval [a, b] satisfying:

Then there exists a value x = c such that f'(c) = .

Calculation:

The given function f(x) = is both differentiable and continuous in the interval [1, 3].

f'(x) =

By the Mean Value Theorem, there exists a c ∈ [1, 3], such that:

f'(c) =

⇒

⇒ c = √3.