The point where the first derivative of the function is 0 is called the stagnation point of the function, and the stagnation point can divide the monotonous interval of the function. (stagnation point is also called stable point, critical point.

Mathematically, an inflection point refers to a point that changes the upward or downward direction of a curve. Intuitively speaking, the inflection point is the point where the tangent intersects the curve (that is, the concave-convex boundary point of the curve). If the function of the graph has a second derivative at the inflection point, then the second derivative must be zero or nonexistent.

Extended data:

The inflection point is the point where the sign of the derivative changes. The inflection point can be a relative maximum or a relative minimum (also called local minimum and maximum). If the function is differentiable, then the inflection point is the fixed point.

However, not all fixed points are inflection points. If the function is differentiable twice, then the fixed point of the fixed point is the horizontal inflection point. For example, the function x3 has a fixed point at x = 0, which is also an inflection point, but not a turning point.

The monotonicity of stagnation point may change, the monotonicity of inflection point may also change, and the concavity and convexity will inevitably change.

References:

Baidu encyclopedia-stagnation point

References:

Baidu encyclopedia-turning point