Linked from

The 20 pages that link to Taylor's theorem, each with the reason it gives.

• Taylor seriesRelated: Its remainder term quantifies the error when a Taylor series is truncated.

• DifferentiabilityRelated: Higher derivatives strengthen local approximation beyond the first-order linear case.

• Hessian matrixRelated: The Hessian supplies the quadratic term in the local approximation.

• Radius of convergenceRelated: The convergence radius helps determine where an infinite Taylor expansion can represent a function.

• Mean value theoremRelated: Its remainder estimates are proved using repeated applications of the mean value theorem.

• Fréchet derivativeRelated: The Fréchet derivative supplies the first-order term in Taylor expansions on normed spaces.

• Rolle's theoremRelated: Rolle's theorem is used in deriving common forms of the Taylor remainder.

• Second derivative testRelated: Its local expansion explains why the quadratic term determines behavior when the first derivative vanishes.

• L'Hôpital's ruleRelated: Taylor expansions can expose the leading terms behind limits the rule evaluates.

• Bernoulli's inequalityRelated: Bernoulli's bound is a one-sided first-order estimate for a power function.

• Differentiable functionRelated: Differentiability of higher orders enables increasingly accurate local polynomial models.

• Guillaume de l’HôpitalRelated: Taylor expansions provide another way to analyze limits that the rule can evaluate.

• Itô's lemmaRelated: A second-order expansion explains why squared Brownian increments survive.

• Cauchy's mean value theoremRelated: Cauchy’s theorem is used in proofs that establish forms of Taylor’s remainder.

• Brook TaylorRelated: Taylor’s 1715 treatise gave an early general statement of this result.

• Cauchy's formula for repeated integrationRelated: Repeated integration of a derivative yields the integral remainder's power-weighted kernel.

• Series expansionRelated: Its remainder estimates quantify the error from truncating a local expansion.