 ### Average Rate of Change Over an Interval – Definition and Examples

This article explores the concept of the average rate of change over an interval, aiming to illuminate this mathematical tool in a manner accessible to everyone. Defining Average Rate of Change Over an Interval The average rate of change over an interval refers to the change in the value of a function between two points […]

### Inverse Variation Equation – Definition and Examples

Inverse variation equations represent a captivating class of mathematical relationships that embody a distinct form of interdependence. When an inverse variation equation links two variables, an increase in one leads to a corresponding decrease in the other, and vice versa. This article will explore the mathematical elegance and practical importance inherent to inverse variation equations. […]

### Derivative of ln(2X) – Definition and Examples

This article will focus on an intriguing task – finding the derivative of ln(2x) (the natural logarithm function). As one of the cornerstone concepts in calculus, the derivative serves as a powerful tool in deciphering the rate of change or the slope of a function at any point. Defining Derivative of ln(2x) The derivative of […]

### Rolle’s Theorem – Explanation and Examples

Rolle’s theorem states that if a real-valued function is continuous in a closed interval $[a,b]$ and is differentiable on the open interval $(a,b)$ while $f(a) = f(b)$, then there must be a point “$c$” in the open interval $(a,b)$ such that $f'(c) = 0$. The graphical representation of Rolle’s theorem is given below. Read moreFunction […]

### Points That Lie on the Same Line – Definition and Examples

Welcome to exploring the fundamental principles of geometry, focusing on the intriguing concept of points that lie on the same line. In this article, we’ll dive deep into the principles of lines in two-dimensional and three-dimensional spaces, the tests for the points that lie on the same line, essential theorems, and the pervasive influence of […]