- #1

- 171

- 0

## Homework Statement

Being a>0 and f:[a,b]--->R continuos and differentiable in (a,b), show that there exists a t ##\in## (a,b) such that:

## \frac{bf(a)-af(b)}{b-a}=f(t)-tf'(f)##

## The Attempt at a Solution

For lagrange's theorem, we have:

## \frac{f(a)-f(b)}{b-a}= -f'(t) ##

thought i could find f(t) from the equation ##f(x) = f(t) + f'(t)(x-t)+R_1(x-t)## ignoring R.

but then a "x" would appear and I don't know how to deal with it.

Last edited by a moderator: