Complex function question: f(z) is differentiable on region D. Inside D there is a line segment C with end points a and b.

[yma16]

f(z) is differentiable on region D. Inside D there is a line segment C with end points a and b. Proof that there is a number k, |k|<=1 and a point p on C such that

f(b)-f(a)=k(b-a)f'(p)

Thank you.

 

[The Highlander]

f(z) is differentiable on region D. Inside D there is a line segment C with end points a and b. Proof that there is a number k, |k|<=1 and a point p on C such that

f(b)-f(a)=k(b-a)f'(p)

Thank you.

So, do you have a question to ask?

Or are you just posting this problem expecting someone here to complete it and post the answer for you?

It looks like you've been here long enough to know that's not likely to happen.

What have you tried?

Show us your attempt at solving the problem and say where you got stuck.

Then help may be offered.