# Don't understand use of auxiliary function in proving theorems

• November 17th 2010, 09:09 PM
Don't understand use of auxiliary function in proving theorems
How was the auxiliary function to be used in proving the theorem below determined? I don't understand why this function was chosen, and how the author arrived at the decision of choosing this function? This is the first time I came across the use of auxiliary functions in proving a theorem, so I am a bit confused whether the function is chosen by pure intuition or is there a method behind this.
http://www.mathhelpforum.com/math-he...3&d=1290060131
Attachment 19753
• November 17th 2010, 11:41 PM
FernandoRevilla
Quote:

The important thing is that $F$ works and you understand why works. All the same, in this case, analyze:
1.- $G(x)=f(x)-f(a)$ translates vertically the graph of $f$ in such a way that $G(a)=0$ .
2.- The equation of the straight line containing the endpoints of the $G$ graph is:
$y=\dfrac{f(b)-f(a)}{b-a}(x-a)$