Suppose that f and g are continuous on [a, b] and differentiable on (a, b). Suppose also that f(a) =g(a) and f′(x)< g′ (x) for a < x < b. Prove that f(b)< g(b). [Hint: Apply the Mean Value Theorem to the function h=f−g.]
Suppose that f and g are continuous on [a, b] and differentiable on (a, b). Suppose also that f(a) =g(a) and f′(x)< g′ (x) for a < x < b. Prove that f(b)< g(b). [Hint: Apply the Mean Value Theorem to the function h=f−g.]