My favorite theorem is La grange's Mean Value Theorem . I like it because its quite simple but has many far fetched applications and is one of the most fundamental theorems of calculus. The theorem states that:

Let $ f(x) $ be a function of x subject to:

                    a. $ f(x) $ is a continuos function of x in the closed interval $ a<=z<=b $.
                    
                     b. $ f'(x) $ exists for every point in the open interval a<x<b, then there exists at least one value of x, say c such that $ a<c<b $ where
                               
                                        $ f'(c)=\frac{f(b)-f(a)}{b-a} $.

Rolle's theorem is a special case of this theorem.

More information about when it was first described and its applications can be found here and also here .

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett