question_answer 1)

Let f be a function defined on [a, b] such that  Then prove that f is an increasing function on (a, b).  

Answer:

Let x1, x2  such that x1 < x2.       Since  f(x) satisfies both conditions of L.M.V. theorem, therefore there exists a point  such that                                                    Thus, we have x1 < x2             Hence f(x) is an increasing function in (a, b).