Solution of inflection point of curve: 1, f''(x). 2. Let f''(x) = 0 and be realistic. 3. If f''(x) has different symbols near x0, x0 is the inflection point of the curve, otherwise it is not.

1, definition of inflection point:

Mathematically, an inflection point refers to a point that changes the upward or downward direction of a curve. Intuitively, 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, the characteristics of inflection point:

① There are two intersections between the tangent at the inflection point and the curve.

② The monotonicity of the function changes at the inflection point.

③ At the inflection point, the function value changes from increasing to decreasing or from decreasing to increasing.

Application of curve inflection point;

1, financial investment strategy:

The inflection point theory is widely used in the formulation of financial investment strategies. Investors can use the inflection point to judge the turning point of market trends, so as to adjust their investment strategies. When the market price rises or falls for a long time, once there is an inflection point, it means that the market trend may reverse.

2. Stock price forecast:

The inflection point theory can also be used to predict the stock price. By analyzing the historical data of stock price, investors can find the inflection point of stock price and predict the future stock price trend.

3, economic cycle analysis:

The inflection point theory also has application value in economic cycle analysis. At different stages of the economic cycle, economic growth rate, inflation rate and other indicators will have different characteristics. By judging the emergence of inflection point, we can accurately judge the stage of economic cycle and formulate corresponding macroeconomic policies.

4, industry cycle analysis:

The inflection point theory can also be applied to industry cycle analysis. Different industries will go through different life cycle stages in different periods, from growth to maturity and then to recession. By judging the inflection point of the industry cycle, we can formulate corresponding investment strategies and business strategies.

5, enterprise development analysis:

In the analysis of enterprise development, inflection point theory also has certain application value. The development of an enterprise will go through different stages, from the initial stage to the growth stage to the maturity stage and then to the recession stage. By judging the inflection point of enterprise development, we can accurately judge the future development trend of enterprises, so as to formulate corresponding strategic planning and management measures.