Mathematically, concavity, concavity, convexity and convexity are collectively called convexity of curves, which refers to the graphic style in the plane coordinate system:

1, the curve with upward opening is called concave or convex, and its shape is ∨;

2. The curve with downward opening is called concave or convex, and its shape is ∩;

3. Therefore, there are four kinds of concave, concave, convex and convex, which can actually be divided into convex and convex:

(1) From the tangent point of view, the tangent of any point on the lower convex arc is below the curved arc, and the tangent of any point on the upper convex arc is above the curved arc.

(2) From the secant point of view, if the secant segments of any two points of the continuous curve y=f(x) on the curve arc corresponding to the interval (a, b) are above the curve arc between these two points, the curve arc is said to be convex downward, and the function y=f(x) on the interval (a, b) is said to be convex downward (or concave upward, that is, the curve opening is upward). On the contrary, it is convex.

(3) From the point of derivative, let y=f(x) have a second derivative in (a, b), if f'' (x) is in (a, b >；; O, then y=f(x) is convex in (a, b); If in (a, b) f'' (x)