Increasing and decreasing functions

When it comes to mathematics, the branch of study known as calculus deals with continuous change. “The calculus of infinitesimals” is another name for calculus, which is also referred to as “infinitesimal calculus”. In its most basic definition, classical calculus is the study of continuous change in the behaviour of mathematical functions. For example, velocity […]

Introduction: Synthetic division is one of the ways to manually perform Euclidean division of polynomials in algebra. Polynomial division can also be done using the long division approach. Synthetic division, on the other hand, takes less writing and computations than the long division technique of polynomials. For the exceptional instances of dividing by a linear

Introduction A rule that assigns each element in X to exactly one element in Y is called a function. If a variable y is associated with an independent variable x that there is a rule that determines a unique value of y whenever a numerical value is assigned to x, then y is said to

It is possible to calculate the derivative of a function of a real variable in mathematics by measuring the sensitivity of the function value (output value) to changes in its argument (input value). Calculus’s derivatives are a fundamental tool for problem-solving. A good example is the derivative of the position of a moving object with

Successive differentiation: In scientific and engineering applications, higher-order differential coefficients are critical. Consider the function y=f(x) as a function of x. The derivative or first derivative of y with respect to x is defined as the result of differentiation y with respect to x, and it is symbolised by dy/dx. The outcome of differentiating f′(x)

Differentiation is needed to find the rate of change. It all starts with the differentiation of a single variable to a higher order of variables.  In a graph, it is indicated by the slope of a tangent line to the function at any point. Differentiation is applicable to several different variables. It can be done

In science, a formula, such as a mathematical formula or a chemical formula, is a brief way to convey information symbolically. The basic concept of a connection between specified quantities is referred to as a formula in informal science use. Formulas, which derives from the most prevalent plural noun form in English, or formulae, which

Indeterminates and constants are found in polynomials, which are algebraic expressions. Polynomials may be thought of as a type of mathematics. They’re used to express numbers in practically every discipline of mathematics, and they’re particularly significant in others, like calculus. 2x + 9 and x² + 3x + 11 are polynomials, for example. Definition of Polynomial

The basic rule In the case of polynomials and rational functions, the building blocks are the functions f(x)=c and g(x)=xn, where n is a positive integer. These are the building blocks from which all polynomials and rational functions are constructed. For the purpose of effectively determining the derivatives of polynomials and rational functions without having

Introduction  Rolle’s theorem is defined as the special case of the mean value theorem which states that if ‘f’ is a real-valued function defined on the closed interval [a, b] and  is differentiable in the open interval (a, b) where ( a<x<b) and f(a)= f(b), then there would be at least one value of c