Mean value theorem
The mean value theorem is a fundamental theorem in calculus. It states that if a function is continuous on a closed interval and differentiable on the open interval within that closed interval, then there exists at least one point where the instantaneous rate of change of the function is equal to the average rate of change of the function over that interval.
About
It states that if a function is continuous on a closed interval and differentiable on the open interval within that closed interval, then there exists at least one point where the instantaneous rate of change of the function is equal to the average rate of change of the function over that interval. The theorem is named after mathematician Augustin-Louis Cauchy, who first proved it in the 19th century. It has many applications in various fields, including physics, economics, and engineering. The mean value theorem is often used to prove other important results in calculus, such as the first and second derivative tests for determining the behavior of a function.