To prepare for next week

First: Seminar problem assignment updated.

I have not yet made a new 2019 note on convexity/concavity/quasi-*. The C^2 characterization is covered already, but we will get as far as to the C^1 characterization and beyond. You should have a look at the note up to the C^1 characterization.

Then, quasiconvex functions: have a look at this plot. The function is not convex, it flattens out: fill with water up high enough, and a line segment from the bottom to the shore will cut outside. But it is quasiconvex: 

• Fill up to level L (fixed, but arbitrary). 
• Look down at the water surface from a bird's view. 
• For this particular function, the water surface will be an elliptic disc (that is, an ellipse and its inside); that is a convex set.