Taylor's Inequality

Taylor's inequality is an estimate result for the value of the remainder term in any -term finite Taylor series approximation.

Indeed, if is any function which satisfies the hypotheses of Taylor's theorem and for which there exists a real number satisfying on some interval , the remainder satisfies

on the same interval .

This result is an immediate consequence of the Lagrange remainder of and can also be deduced from the Cauchy remainder as well.