Linked from

The 10 pages that link to Mean value theorem, each with the reason it gives.

• Real analysisBroader topic: It connects derivative bounds to global behavior, including monotonicity and error estimates.

• DifferentiabilityRelated: Differentiability on the interval’s interior is one of its central hypotheses.

• Intermediate value theoremRelated: It gives a specific derivative value between endpoint data, while this theorem concerns function values.

• Taylor's theoremNarrower topic: The Lagrange remainder is obtained by extending the mean-value principle to higher derivatives.

• Monotonic functionRelated: It converts a consistent derivative sign into an order relation between function values.

• Bounded functionRelated: A derivative bound yields a Lipschitz estimate, which can control function variation.

• Rolle's theoremNarrower topic: Rolle's theorem is the special case where the average rate of change is zero.

• Linear approximationRelated: It connects a tangent slope to the secant slope, but does not itself provide a local estimate.

• Cauchy's mean value theoremNarrower topic: Cauchy’s result extends the familiar single-function theorem to a pair of functions.

• Interior extremum theoremRelated: Its proof framework also relies on Rolle’s theorem and vanishing derivatives at extrema.