This is the absolute value of the derivative:
.
Graph it to see that it is bounded.
From the mean value theorem:
.
Let f : R ->R be a function.
We say that f is Lipschitz continuous if there is some
L > 0 such that |f(x) − f(y)| < L|x − y| for all x, y in R.
I want to show that f : R ->R defined as f(x) = x^2 / (1+ x^2)is Lipschitz continuous.
I know I should use the Mean Value Theorem but i cant seem to apply it can some one please help thanks