In mathematics, the mean value theorem (or Lagrange's mean value theorem) states, roughly, that for a given planar arc between two endpoints, there is...

In mathematics, Vinogradov's mean value theorem is an estimate for the number of equal sums of powers. It is an important inequality in analytic number...

In mathematical analysis, the mean value theorem for divided differences generalizes the mean value theorem to higher derivatives. For any n + 1 pairwise...

rod. The mean value theorem gives a relationship between values of the derivative and values of the original function. If f(x) is a real-valued function...

{\displaystyle f'(c)=0.} 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...

dt.} By the first part of the theorem, we know G is also an antiderivative of f. Since F′ − G′ = 0 the mean value theorem implies that F − G is a constant...

value theorem states that if f {\displaystyle f} is a continuous function whose domain contains the interval [a, b], then it takes on any given value...

calculus, the mean of a function is loosely defined as the ”average" value of the function over its domain. In a one-dimensional domain, the mean of a function...

arithmetic mean of the left and right derivatives at that point, if the latter two both exist.: 6  Neither Rolle's theorem nor the mean-value theorem hold for...

formula Cauchy's mean value theorem in real analysis, an extended form of the mean value theorem Cauchy's theorem (group theory) Cauchy's theorem (geometry)...

Taylor's theorem are usually proved using the mean value theorem, whence the name. Additionally, notice that this is precisely the mean value theorem when...

Proof 2. The second proof is based on combining the mean value theorem and the intermediate value theorem. Define c = 1 2 ( a + b ) {\displaystyle c={\frac...

\over (t+x)\,(t+y)}.} One can generalize the mean to n + 1 variables by considering the mean value theorem for divided differences for the n-th derivative...

necessarily has value 0) at an isolated zero of f ( z ) {\displaystyle f(z)} . Another proof works by using Gauss's mean value theorem to "force" all points...

convergence theorem and the mean value theorem (details below). We first prove the case of constant limits of integration a and b. We use Fubini's theorem to change...

A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several...

including the mean value theorem (over geodesic balls), the maximum principle, and the Harnack inequality. With the exception of the mean value theorem, these...

In mathematics, the root mean square (abbrev. RMS, RMS or rms) of a set of values is the square root of the set's mean square. Given a set x i {\displaystyle...

the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard...

is a consequence of the Hahn-Banach theorem and generalizes the mean value theorem for integrals of real-valued functions: If V = R {\displaystyle V=\mathbb...

the interval. The value g(x)-g(y) is always nonzero for distinct x and y in the interval, for if it was not, the mean value theorem would imply the existence...

}(0)=I} , so that a = b = 0 {\displaystyle a=b=0} . By the mean value theorem for vector-valued functions, for a differentiable function u : [ 0 , 1 ] →...

four-square theorem, which states that every positive integer can be expressed as the sum of four squares of integers Mean value theorem in calculus The...

value theorem Differential equation Differential operator Newton's method Taylor's theorem L'Hôpital's rule General Leibniz rule Mean value theorem Logarithmic...

In multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables. It does...

which is obtained from the mean value theorem by equating the function values at the endpoints. Corollary Fundamental theorem Lemma (mathematics) Toy model...

theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem,...

the result. A further generalization of the theorem was proven by Fréchet (1906), to sets of real-valued continuous functions with domain a compact metric...

Conversely, instead of using the generalized mean value theorem in the second proof, the classical mean valued theorem could be used. The properties of repeated...

interpolation formula Lagrange–Bürmann formula Triple product expansion Mean value theorem Euler–Lagrange equation This disambiguation page lists mathematics...