Mean Value Theorem Question

Thanks. Without the bestfit curve, I was struggling.

[Eeegah]

So anyway, let L be the line between (a,f(a)) and (b,f(b)). Note that L(a)=a and L(b)=b. But this means L(a)-f(a)=L(b)-f(b)=0, and so we can apply Rolle's Theorem: there exists c in [a,b] such that [L(c)-f(c)]'=0. With some manipulation then we have

L'(c)-f'(c)=0
L'(c)=f'(c) *

But L'(c)=[f(b)-f(a)]/(b-a), and so we're done. Note that * is what you actually posted, which is directly equivalent.

I only needed help for oneline of the proof this time I'm so proud ^_________^