Show that if f$\displaystyle \in$$\displaystyle C^2$[a,b], then for $\displaystyle x_1$,$\displaystyle x_2$$\displaystyle \in$[a,b], there exists $\displaystyle \xi$$\displaystyle \in$[a,b], so that f '($\displaystyle x_1$)=(f($\displaystyle x_2$)-f($\displaystyle x_1$)/($\displaystyle x_2$-$\displaystyle x_1$) )-(($\displaystyle x_2$-$\displaystyle x_1$)/2) f''($\displaystyle eta$)

To do this, do I have to show the proof? If so what is the proof?