Applications of Derivatives

Calculus allows one to determine both maximums and minimums by applying the concept of derivatives. Because we are familiar with the idea that the derivatives provide information about the gradient and the slope of the function, we are able to identify the points along with the function at which the gradient is zero. These points […]

The extrema of a function are the points at which the function reaches its maximum and minimum values. The maximum and minimum values of a function are the maximum and minimum values of the function within the supplied set of ranges, respectively. Under the whole range of the function, the absolute maxima and minima of

INTRODUCTION In mathematics, the maxima and minima of a function is called extrema. The highest point within the given range on the curve is called maxima point.The lowest point within the given range on the curves is called minima point. The extremum is found using the calculus of variation  if an extremum consists of its

When we use mathematical ideas to ‘model’ an object or situation from the real world, we are creating a Math Model. This can help us understand the real world and can be used to improve many aspects of our lives. Mathematical models are an essential part of the working world, from safety to planning and

The least-square approach involves minimising the sum of the squares of the offsets (residual component) of the points from the curve to get the best-fitting curve or line of best fit for a group of data points. The trend of outcomes is statistically evaluated throughout the process of determining the relationship between two variables. Regression

The role mean value theorem is extended by the Lagrange mean value theorem. According to the theorem, there exists a point on a curve between two points where the tangent is parallel to the secant line passing between these two points. The lone mean value theorem is another name for the Lagrange mean value theorem.

A factor is a number that divides a given number exactly in mathematics. A factor is also known as the divisor of a given number in another way. A factor divides a given number by zero and leaves a remainder. The multiplication or division methods can be used to find the factor of any number.

A function is guaranteed to have both a maximum and a minimum value by the Extreme Value Theorem, provided that certain requirements are met.  Establishing that the function is continuous on the closed interval is the first step in the process of applying the Extreme Value Theorem.  This is done so that the results of

The squeeze theorem is a theorem about the limit of a function caught between two other functions in calculus. In calculus and mathematical analysis, the squeeze theorem is used to validate the limit of a function by comparing it to two other functions whose limits are known. It was initially utilised geometrically by the mathematicians

Clairaut’s equation is a differential equation in mathematics with the form y = x (dy/dx) + f(dy/dx), where f(dy/dx) is a function of just dy/dx. The equation is named after Alexis-Claude Clairaut, a French mathematician and physicist who invented it in the 18th century. He took part in an excursion to Lapland in 1736 with