7.3 Mean Value Theorem

. Mean Value Theorem Mean value theorem establishes the existence of a point, in between two points, at which the tangent to the curve is parallel to the secant joining those two points of the curve. We start this section with the statement of the intermediate value theorem as follows : Theorem . (Intermediate value theorem) If f is continuous on a closed interval [ , ] a b , and c is any number between f a ( ) and f b inclusive, then there is at least one number x in the closed interval [ , ] a b , such that f x ( ) =