Monotonic functionIn mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysisIn calculus, a function f{\displaystyle f} defined on a subset of the real numbers with real values is called monotonic if it is either entirely non-decreasing, or entirely non-increasing.
Saddle pointIn mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function. An example of a saddle point is when there is a critical point with a relative minimum along one axial direction (between peaks) and a relative maximum along the crossing axis. However, a saddle point need not be in this form.
Maximum and minimumIn mathematical analysis, the maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically as extrema, they may be defined either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema) of a function. Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions.
Concave functionIn mathematics, a concave function is one for which the function value at any convex combination of elements in the domain is greater than or equal to that convex combination of those domain elements. Equivalently, a concave function is any function for which the hypograph is convex. The class of concave functions is in a sense the opposite of the class of convex functions.
Critical point (mathematics)In mathematics, a critical point is the argument of a function where the function derivative is zero (or undefined, as specified below). The value of the function at a critical point is a critical value. More specifically, when dealing with functions of a real variable, a critical point is a point in the domain of the function where the function derivative is equal to zero (also known as a stationary point) or where the function is not differentiable.Function (mathematics)In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time.
DerivativeInstantaneous rate of change (mathematics)The graph of a function, drawn in black, and a tangent line to that graph, drawn in red. The slope of the tangent line is equal to the derivative of the function at the marked point.The derivative at different points of a differentiable function. In this case, the derivative is equal to sin(x2)+2x2cos(x2){\displaystyle \sin \left(x^{2} ight)+2x^{2}\cos \left(x^{2} ight)}.
Interior extremum theoremIn calculus and real analysis, the interior extremum theorem states that any local extremum of a real function at which it is differentiable is a stationary point. It is also known as Fermat's theorem, named after the French mathematician Pierre de Fermat. The interior extremum theorem gives a necessary, but not sufficient condition for local extrema at which the function is differentiable, as some stationary points are not local extrema.
Parity (mathematics)In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not. For example, −4, 0, and 82 are even numbers, while −7, 5, and 23 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers with fractions or decimals such as 1⁄2 or 7.2742.CalculusCalculus is the branch of mathematics that studies continuous change, and is the principal precursor of modern mathematical analysis. Originally called infinitesimal calculus or the calculus of infinitesimals, it has two major branches, differential calculus and integral calculus. Differential calculus studies instantaneous rates of change and slopes of curves; integral calculus studies accumulation of quantities and areas under or between curves.*As an Amazon Associate I earn from qualifying purchases.