1, inflection point, also known as inflection point, mathematically refers to the point that changes the upward or downward direction of the curve. Intuitively speaking, the inflection point is the point where the tangent intersects the curve (that is, the boundary point between the concave arc and the convex arc of a continuous curve). If the function of the graph has a second derivative at the inflection point, the second derivative has a different sign (from positive to negative or from negative to positive) or does not exist at the inflection point.

2. For the image of two-dimensional function, the tangent plane of the stagnation point is parallel to the xy plane. It is worth noting that the stagnation point of a function is not necessarily the extreme point of this function (considering that the sign of the first derivative around this point is unchanged).

3. On the contrary, in a given area, the extreme points of a function are not necessarily the stagnation point (considering the boundary conditions), stagnation point (red) and inflection point (blue) of this function, and the stagnation point of this image is the local maximum or local minimum.