Standard Version of The Theorem
If a real-valued function ƒ is continuous on a closed interval, differentiable on the open interval (a, b), and ƒ(a) = ƒ(b), then there exists a c in the open interval (a, b) such that
This version of Rolle's theorem is used to prove the mean value theorem, of which Rolle's theorem is indeed a special case. It is also the basis for the proof of the Taylor's theorem.
Read more about this topic: Rolle's Theorem
Famous quotes containing the words standard, version and/or theorem:
“I find it interesting that the meanest life, the poorest existence, is attributed to God’s will, but as human beings become more affluent, as their living standard and style begin to ascend the material scale, God descends the scale of responsibility at a commensurate speed.”
—Maya Angelou (b. 1928)
“Exercise is the yuppie version of bulimia.”
—Barbara Ehrenreich (b. 1941)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)