constraints on the term structure, smile slope and smile convexity of the implied volatility surface

I have been a professional options trader for over 11 years. In my experience most options traders fail, and for two reasons: naive faith in mathematical models and software, and a basic misunderstanding of the concept of implied volatility.

Describe and explain  the constraints on the term structure, smile slope and smile convexity of the implied volatility surface. Give a numerical example of each in terms of option prices.