What Is an Inflection Point?

The inflection point, also called the 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 that makes the tangent cross the curve (that is, the boundary point between the concave arc and the convex arc of the continuous curve). If the function of the curve graph has a second derivative at the inflection point, the second derivative at the inflection point has a different sign (from positive to negative or negative to positive) or does not exist.

Let the function y = f (x) be at the point

Continuous in a neighborhood of, if (

, F (

)) Is the boundary between concave and convex of the curve y = f (x), then (

, F (

)) Is the inflection point of the curve y = f (x). ^[1]

The following steps can be used to determine the inflection point of the continuous curve y = f (x) on the interval I:

Find f '' (x);

Let f '' (x) = 0, solve the real root of this equation in interval I, and find the point where f '' (x) does not exist in interval I;

(3) For each point where the real root or second derivative found in does not exist

And check f '' (x) in

The symbols on the left and right are adjacent, then when the symbols on the two sides are opposite, the dot (

, f (

)) Is the inflection point. When the symbols on both sides are the same, the point (

, f (

)) Not an inflection point.