Increasing and decreasing functions

A composite function is a combination of two different functions to produce a third function. Let us consider two functions u(x) and v(x). In this v(x) is acting first and then the u(x). It is written as u(v(x)) or u∘v(x). In composite functions, the output of the inner function becomes the input of the outer […]

The Leibnitz rule for derivative of the antiderivative is essentially what this theorem is about. In accordance with the rule, the derivative in nth order of the product of two functions may be stated mathematically with the assistance of an equation. Antiderivatives (also known as primitives) of a function are functions that might have been

Calculus employs the product rule to differentiate functions. The product rule is employed when a given function is the product of two or more other functions. If the issues are a combination of two or more functions, the product rule can be used to find their derivatives. Simply put, the term “product” refers to the

Let us take a step back and define what a first derivative is in order to better comprehend the second-order derivative. The first derivative is referred to as  dy/dx  reflects the pace at which the value of y changes in relation to the value of x Consider the following example: if a car travels 60

Introduction: Let f(t) is a function defined for all positive values of t. Then the Laplace Transforms of f(t) is given by L(f(t)) or f`(s) is defined as Sufficient conditions for the existence of Laplace Transform of a function: The function f(t) must satisfy the following conditions for the existence of the Laplace Transform The

Rolle’s Theorem is a special case of the mean value theorem that is true if and only if specific conditions are met. At the same time, Lagrange’s mean value theorem is the mean value theorem itself, or the first mean value theorem, as the term is used in the literature. In general, mean can be

The inverse function theorem in mathematics, specifically differential calculus, states that a function is invertible in the neighborhood of a point in its domain if its derivative is continuous and non-zero at the point. The theorem also provides a formula for the inverse function’s derivative. This theorem can be generalized in multivariable calculus to any

As the name implies, the exponential function contains an exponential. However, an exponential function has a constant as the base and a variable as the exponential, but not the other way around (if the function has a variable as the base and a constant as the exponential, it is a power function, but it is

Interpolation is a statistical strategy for estimating an unknown price or possible yield of an asset using related known variables. Interpolation is done by using other known values that are in the same order as the unknown value. Interpolation is, at its core, a straightforward mathematical notion. If a group of data points has a

We learned in differentiation that if a function f is differentiable in an interval, say I, we get a set of a family of values for the functions in that interval. Is there any way to determine the function’s properties if the function’s values within an interval are known? Integration is a mathematical concept that