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function with vanishing derivative

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  • Auxiliary function — In mathematics, auxiliary functions are an important construction in transcendental number theory. They are functions which appear in most proofs in this area of mathematics and that have specific, desirable properties, such as taking the value… …   Wikipedia

  • Functional derivative — In mathematics and theoretical physics, the functional derivative is a generalization of the directional derivative. The difference is that the latter differentiates in the direction of a vector, while the former differentiates in the direction… …   Wikipedia

  • Cantor function — In mathematics, the Cantor function, named after Georg Cantor, is an example of a function that is continuous, but not absolutely continuous. DefinitionThe Cantor function c : [0,1] → [0,1] is defined as follows:#Express x in base 3. If possible …   Wikipedia

  • Generalized function — In mathematics, generalized functions are objects generalizing the notion of functions. There is more than one recognised theory. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and (going …   Wikipedia

  • Characteristic function (probability theory) — The characteristic function of a uniform U(–1,1) random variable. This function is real valued because it corresponds to a random variable that is symmetric around the origin; however in general case characteristic functions may be complex valued …   Wikipedia

  • Mollifier — A mollifier (top) in dimension one. At the bottom, in red is a function with a corner (left) and sharp jump (right), and in blue is its mollified version. In mathematics, mollifiers (also known as approximations to the identity) are smooth… …   Wikipedia

  • Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… …   Wikipedia

  • Affine connection — An affine connection on the sphere rolls the affine tangent plane from one point to another. As it does so, the point of contact traces out a curve in the plane: the development. In the branch of mathematics called differential geometry, an… …   Wikipedia

  • Logarithm — The graph of the logarithm to base 2 crosses the x axis (horizontal axis) at 1 and passes through the points with coordinates (2, 1), (4, 2), and (8, 3) …   Wikipedia

  • Integral — This article is about the concept of integrals in calculus. For the set of numbers, see integer. For other uses, see Integral (disambiguation). A definite integral of a function can be represented as the signed area of the region bounded by its… …   Wikipedia

  • Taylor's theorem — In calculus, Taylor s theorem gives a sequence of approximations of a differentiable function around a given point by polynomials (the Taylor polynomials of that function) whose coefficients depend only on the derivatives of the function at that… …   Wikipedia

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