Question

If f(x) and g(x) are continuous in [a, b] and differentiable in (a, b), show that there exists some c ∈ (a, b) such that

Answer 1

Let

Since f(x) and g(x) are continuous in [a, b] and differentiable in (a, b), so h(x) is continuous in [a, b] and differentiable in (a, b). 

Thus, by L.M.V. Theorem, there some c in (a, b)