Notes on Lecture 14

A proof of the inequality we used (courtesy Danny):

To prove: Log[1 + b] >= 2 b/(2 + b) for b>=0
Note that it's equal when b=0.
You take the derivative of
Log[1 + b] - 2 b/(2 + b), and get
b²/((1 + b) (2 + b)²). This is non-negative
for b>=0. QED.