The mean value theorem states that in a closed interval, a function has at least one point where the slope of a tangent line at that point (i.e. the derivative) is equal to the average slope of the function (or the secant line between the two endpoints). Ergo: on a closed interval has a derivative at point , which has an equivalent slope to the one connecting and . Therefore, the derivative equals the slope formula: There are three formulations of the mean value theorem: