(e) f(x1, x2) = max{ f1(x1, x2), f2(x1, x2)} where f1(x1, x2) = 4x12 + 2x22 and f2(x1, x2) = 2x12 – 3x2 is a convex, concave, or neither?

Both of them are convex functions

Step-by-step explanation:

The twin notions of concavity and convexity in the mathematics or economics, but they are used widely in economic theory, and are also central to optimization theory.Firstly, a concave  function of a single variable is if every line segment joining two points on its graph does not lie above the graph at any point. In turn, a convex function of a single variable is  if every line segment joining two points on its graph does not lie below the graph at any point. Then please find the attached excel file with more detailed description and explanation with the graphs.

(-5,-28)

i graphed to on desmos.