The Strawberry Theorem
In economics one knows that break-even points are critical points of the average cost. Mathematically f=g if and only if g'=0 if g=F/x and F'=f. The proof is obtained by computing (F/x)' using the quotient rule.
The result is also known as the Strawberry theorem as it was illustrated with the cost of Strawberriies in Heckner/Kretschmer's book "Don't worry about Micro!" It is a sweet theorem!