Results 221 to 230 of about 64,585 (262)
Some of the next articles are maybe not open access.
2014
The main focus of this chapter is the Mean Value Theorem and some of its applications. This is the big theorem in the world of differentiable functions. Many important results in calculus (and well beyond!) follow from the Mean Value Theorem. We also look at an interesting and useful generalization, due to Cauchy.
openaire +1 more source
The main focus of this chapter is the Mean Value Theorem and some of its applications. This is the big theorem in the world of differentiable functions. Many important results in calculus (and well beyond!) follow from the Mean Value Theorem. We also look at an interesting and useful generalization, due to Cauchy.
openaire +1 more source
2017
This chapter is dedicated entirely to the Mean Value Theorem and its complex history. The opening section offers modern statements of the Mean Value Theorem and some of its variants, proofs of these results, their interrelations, and some applications. The second section provides to some extent the prehistory of the Mean Value Theorem, from Apollonius ...
openaire +1 more source
This chapter is dedicated entirely to the Mean Value Theorem and its complex history. The opening section offers modern statements of the Mean Value Theorem and some of its variants, proofs of these results, their interrelations, and some applications. The second section provides to some extent the prehistory of the Mean Value Theorem, from Apollonius ...
openaire +1 more source
2012
In elementary calculus we learn the mean value theorem: Let f be a real-valued function defined on a closed bounded interval \( \subset \mathbb{R}\) . If f is continuous on and differentiable on (a,b), then there is a point c e (a,b) such that $$f(b) - f(a) =\dot{ f}(c)(b - a).$$
openaire +1 more source
In elementary calculus we learn the mean value theorem: Let f be a real-valued function defined on a closed bounded interval \( \subset \mathbb{R}\) . If f is continuous on and differentiable on (a,b), then there is a point c e (a,b) such that $$f(b) - f(a) =\dot{ f}(c)(b - a).$$
openaire +1 more source
The Converse of Pólya’s Mean Value Theorem
SIAM Journal on Mathematical Analysis, 1987let L be a linear differential operator of the form \(Lu=u^{(n)}+a_ 1(t)u^{(n-1)}+...+a_ n(t)u,\) which is disconjugate on an interval I, where \(a_ i(t)\), \(i=1,2,...,n\) are continuous real functions on an interval \(J\supset I\). Pólya proved that if v is any n times differentiable function on I which has \(n+1\) zeros, then \(Lv(p)=0\) for some ...
openaire +2 more sources
1986
Giver a curve, y = f(x), we shall use the derivative to give us information about the curve. For instance, we shall find the maximum and minimum of the graph, and regions where the curve is increasing or decreasing. We shall use the mean value theorem, which is basic in the theory of derivatives.
openaire +1 more source
Giver a curve, y = f(x), we shall use the derivative to give us information about the curve. For instance, we shall find the maximum and minimum of the graph, and regions where the curve is increasing or decreasing. We shall use the mean value theorem, which is basic in the theory of derivatives.
openaire +1 more source
The Mean Value Theorem and It’s Application.
Science and Technology of Engineering, Chemistry and Environmental ProtectionThe Mean Value Theorem (MVT) is the central theorem of differential Calculus. It’s the major tool to research on function, also bridging the gap between function and derivative. There are lot of researchers focus on it from ancient times until now. This article introduces details about two mean theorems include the Rolle’s Theorem and Lagrange Theorem.
openaire +1 more source
A stronger version of the second mean value theorem for integrals
Computers and Mathematics With Applications, 2012Roman Wituła +2 more
exaly
The mean value theorems and a Nagumo-type uniqueness theorem for Caputo’s fractional calculus
Fractional Calculus and Applied Analysis, 2012Kai Diethelm, Diethelm Kai
exaly