Rolle’s Theorem and Mean Value Theorem
Rolle’s Theorem: Suppose that y = f(x) is continuous at every point of the closed interval [a, b] and differentiable at every point of its interior (a, b). If f(a) = f(b), then there is at least one number c in (a, b) such that.
The Mean Value Theorem
The Mean Value Theorem is a more general case of Rolle's Theorem. We remove the requirement that f(a) = f(b). We still can draw a line through the points (a, f(a)) and (b, f(b)), but the line is no longer horizontal. But there is a point x = c where the tangent line to y = f(x) at c is parallel to the line through (a, f(a)) and (b, f(b)).
Learn more about Rolle's Theorem and mean value theorem by reading the explanation below.
Rolle’s Theorem and Mean Value Theorem
Practice: Apply the mean value and Rolle’s theorem in the following exercises.
Rolle’s Theorem and Mean Value Theorem 1