I understand that the derivative is bounded, but how does that imply |f(x)-F(y)| < |x-y| ? I have not learn to do anything with derivative in my class yet.
I understand that the derivative is bounded, but how does that imply |f(x)-F(y)| < |x-y| ? I have not learn to do anything with derivative in my class yet.
Sorry to say, someone has gotten the cart before the horse!
This is a classical problem.
It is a Lipschitz Condition. The derivative is bounded.
That implies uniform continuity.
You need to confront your lecturer.