This theorem can be used to prove Taylor's Theorem, of which it is also a generalization of, while a generalized version of this theorem can be used to prove L'hopital's rule. That form states that the quotient of the derivatives of two sections of a function at a certain point is equal to the quotient of the differences of the endpoint values, and is named for Cauchy. A special case is of it states that if a continuous function has the same value at the end points of an interval, its derivative must equal zero on that interval, and is named for Rolle. For 10 points, name this theorem which states that there is a least one point on an interval at which the slope is equal to the average derivative.
This theorem can be used to prove Taylor's Theorem, of which it is also a generalization of, while a generalized version of this theorem can be used to prove L'hopital's rule. That form states that the quotient of the derivatives of two sections of a function at a certain point is equal to the quotient of the differences of the endpoint values, and is named for Cauchy. A special case is of it states that if a continuous function has the same value at the end points of an interval, its derivative must equal zero on that interval, and is named for Rolle. For 10 points, name this theorem which states that there is a least one point on an interval at which the slope is equal to the average derivative.
This theorem can be used to prove Taylor's Theorem, of which it is also a generalization of, while a generalized version of this theorem can be used to prove L'hopital's rule.
mean value theorem