RD Sharma Solutions for Class 12 Maths Chapter 15 Means value Theorems

The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b]. If the derivative of a function f is everywhere strictly positive, then f is a strictly increasing function. Mean Value theorem plays an important role in the proof of Fundamental Theorem of Calculus. Suppose f is continuous on [a,b] and f′ exists and is bounded on the interior, then f is of Bounded Variation on [a,b].