It has been a few months since I started digging deeper into the concepts of Fundamental Calculus. It is interesting to understand the theorems, and their applications in either proving mathematical statements or understanding a mathematical model of a natural phenomenon.
The most potent theorem I have encountered till date is the Mean Value Theorem for continuous and differentiatiable functions.
While I do understand the proof to a good extent, I often find myself unable to realize its applications in several problems. I realize that as a beginner I need more practice.
I was wondering if I could be introduced to several applications( in any field of analysis ) of this theorem. That way, my understanding of this theorem will strengthen significantly.