An inflection point (also known as an inflection point) refers to a point that mathematically 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, the second derivative has a different sign (from positive to negative or from negative to positive) or does not exist at the inflection point.

Existence conditions:

prerequisite

Let the function f(x) have a second-order continuous derivative in a certain neighborhood, if it is the inflection point of the curve, otherwise it will not hold.

The first sufficient condition:

According to the definition of inflection point directly, the first sufficient condition for the existence of inflection point can be obtained.

Let the function f(x) have a second-order continuous derivative in a certain neighborhood, and the signs on both sides are different, which is an inflection point of the curve y=f(x); The same symbol on both sides is not the inflection point of the curve.

Inflection point calculation