中文：

拐点是指函数图像上某点处发生改变方向变化的点。在数学和经济学中，拐点通常被用来描述一个变量由上升转为下降或由下降转为上升的转折点。

在函数图像上，拐点表示函数在这一点上的斜率发生改变，通常伴随着函数的增减性发生改变。在经济学中，拐点通常指经济指标由负增长转为正增长或由正增长转为负增长的转折点。

例如，在人口增长模型中，拐点可能表示人口增长速度由快转为慢或由慢转为快的转折点。在股票市场中，拐点可能表示市场趋势由下跌转为上涨或由上涨转为下跌的转折点。

了解拐点对于预测未来的趋势和变化非常重要。在人口增长模型中，了解拐点可以帮助我们预测未来人口增长的趋势和速度。在股票市场中，了解拐点可以帮助我们预测未来的市场走势和风险。

总的来说，拐点是一个非常重要的概念，可以帮助我们更好地理解和预测未来的趋势和变化。

英文：

The turning point refers to the point at which the direction of change occurs on a function graph. In mathematics and economics, the turning point is often used to describe the moment when a variable shifts from an upward trend to a downward trend or vice versa.

On a function graph, the turning point indicates a change in the slope at that point, often accompanied by a change in the increasing or decreasing trend of the function. In economics, the turning point usually refers to the moment when a economic indicator shifts from negative growth to positive growth or vice versa.

For example, in a population growth model, the turning point may represent the moment when the population growth rate shifts from a fast to slow pace or vice versa. In the stock market, the turning point may indicate a change in market trends from a downward trend to an upward trend or vice versa.

Understanding the turning point is very important for predicting future trends and changes. In a population growth model, understanding the turning point can help us predict future trends and speeds of population growth. In the stock market, understanding the turning point can help us predict future market trends and risks.

Overall, the turning point is a very important concept that can help us better understand and predict future trends and changes.