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

• Nov 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
Thanks a lot for reading.
Attachment 19753
• Nov 17th 2010, 11:41 PM
FernandoRevilla
Quote:

Originally Posted by ssadi
... so I am a bit confused whether the function is chosen by pure intuition or is there a method behind this.

The important thing is that \$\displaystyle F\$ works and you understand why works. All the same, in this case, analyze:

1.- \$\displaystyle G(x)=f(x)-f(a)\$ translates vertically the graph of \$\displaystyle f\$ in such a way that \$\displaystyle G(a)=0\$ .

2.- The equation of the straight line containing the endpoints of the \$\displaystyle G\$ graph is:

\$\displaystyle y=\dfrac{f(b)-f(a)}{b-a}(x-a)\$

Regards.

Fernando Revilla