Answer: concave function: let the function f(x) be defined on [a, b]. If any two points in [a, b] are different, then x 1, x2 holds: f [(x1+x2)/2] > =[f(x 1)+f(x2)]/2 Then f(x) is concave on [a, b].

Function diagram: the arc segment is shaped like a function of ∨, such as y = x 2.

Convex function: Let the function f(x) be defined on [a, b]. X2 is true if there are any two differences in [a, b] x 1: f [(x 1+x2)/2].

Function diagram: the arc segment is shaped like a function of ∩, such as y =-x 2.

F(x)=lgx is a convex function. From the function image, the quadratic function with downward opening is convex and the quadratic function with upward opening is concave.