textbook-theory · English
Rolle's Theorem and the Mean Value Theorem (Section 3.7)
Section 3.7 of an open-source calculus text by Dan Sloughter, covering Rolle's Theorem and the Mean Value Theorem with full proofs. The section establishes that a differentiable function on an interval must attain its average rate of change as an instantaneous rate of change at some interior point, then applies this result to determine intervals of increase and decrease and to prove that two antiderivatives of the same function differ by a constant. Worked examples, geometric interpretations, and a problem set of 16 exercises are included.
Rolle's TheoremMean Value Theoremdifferential calculusantiderivatives