Question

Let f(x) and g(x) be defined and differentiable for x ≥ x₀ and f(x₀) = g(x₀), f '(x) > g '(x) for x > x₀ , then

(a)  f(x) < g(x) for some x > x₀

(b)  f(x) = g(x) for some x > x₀

(c)  f(x) > g(x) for some x > x₀ 

(d)  none of these 

Answer 1

Correct option  (c) f(x) > g(x) for some x > x₀

Explanation:

Consider the function ϕ(x) = f(x) - g(x) on the interval [x₀ , x]. 0 Then, ϕ(x) satisfies all the conditions of Lagrange’s mean value theorem on [x₀ , x].

∴  There exists at least one c ∈ (x₀, x) such that