{\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...

A restricted form of the theorem was proved by Michel Rolle in 1691; the result was what is now known as Rolle's theorem, and was proved only for polynomials...

Michel Rolle (21 April 1652 – 8 November 1719) was a French mathematician. He is best known for Rolle's theorem (1691). He is also the co-inventor in Europe...

this line. The Gauss–Lucas theorem, named after Carl Friedrich Gauss and Félix Lucas, is similar in spirit to Rolle's theorem. If P is a (nonconstant) polynomial...

is what the extreme value theorem stipulates must also be the case. The extreme value theorem is used to prove Rolle's theorem. In a formulation due to...

notions of differential calculus can be found in his work, such as "Rolle's theorem". The mathematician, Sharaf al-Dīn al-Tūsī (1135–1213), in his Treatise...

{\displaystyle g} has n + 1 {\displaystyle n+1} zeros: x0, ..., xn. By applying Rolle's theorem first to g {\displaystyle g} , then to g ′ {\displaystyle g'} , and...

Rolle's theorem, a special case of one of the most important theorems in analysis, the mean value theorem. Traces of the general mean value theorem are...

(calculus) Related rates Regiomontanus' angle maximization problem Rolle's theorem Antiderivative/Indefinite integral Simplest rules Sum rule in integration...

Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law...

Brouwer fixed-point theorem follows almost immediately from the intermediate value theorem. Another example of toy theorem is Rolle's theorem, which is obtained...

complex numbers, named after Marc Voorhoeve. It may be used to extend Rolle's theorem from real functions to complex functions, taking the role that for...

derivative obeys the product and quotient rule has analogs to Rolle's theorem and the mean value theorem. However, this fractional derivative produces significantly...

this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides...

The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated...

In mathematics, the inverse function theorem is a theorem that asserts that, if a real function f has a continuous derivative near a point where its derivative...

Rolle's theorem was given by Michel Rolle in 1691 using methods developed by the Dutch mathematician Johann van Waveren Hudde. The mean value theorem...

The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every...

function, which become generally more accurate as n increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such...

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

In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R...

n → R {\displaystyle \mathbb {R} ^{n}\to \mathbb {R} } ). Multinomial theorem ( ∑ i = 1 n x i ) k = ∑ | α | = k ( k α ) x α {\displaystyle \left(\sum...

{\text{p}} \theta _{0}} . A similar result can be established using Rolle's theorem. The second derivative evaluated at θ ^ {\textstyle {\hat {\theta }}}...

that point, if the latter two both exist.: 6  Neither Rolle's theorem nor the mean-value theorem hold for the symmetric derivative; some similar but weaker...

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through...

and vector calculus, such as the divergence theorem, magnetic flux, and its generalization, Stokes' theorem. Let us notice that we defined the surface...

then it is also a global minimum (use the intermediate value theorem and Rolle's theorem to prove this by contradiction). In two and more dimensions,...

theorem (mathematical analysis) Rising sun lemma (real analysis) Rolle's theorem (calculus) Squeeze theorem (mathematical analysis) Stokes's theorem (vector...

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

{f(x_{1})-f(x_{0})}{x_{1}-x_{0}}}(x-x_{0}).} It can be proven using Rolle's theorem that if f has a continuous second derivative, then the error is bounded...