point of tangent

简明释义

悬挂点

英英释义

例句

1.When analyzing the graph, we focused on finding the point of tangent 切点 for the maximum value.

在分析图形时，我们专注于找到最大值的point of tangent 切点。

2.During the physics class, we learned how to find the point of tangent 切点 on a graph of motion.

在物理课上，我们学习了如何在运动图表上找到point of tangent 切点。

3.The designer ensured that the curves of the logo met at a smooth point of tangent 切点.

设计师确保标志的曲线在一个平滑的point of tangent 切点处相交。

4.In calculus, the slope of the curve at the point of tangent 切点 is crucial for understanding its behavior.

在微积分中，曲线在point of tangent 切点的斜率对于理解其行为至关重要。

5.The architect designed the building to ensure that the roof met the wall at a perfect point of tangent 切点.

建筑师设计了这座建筑，以确保屋顶与墙壁在一个完美的point of tangent 切点相接。

作文

In the realm of mathematics, particularly in calculus, the concept of a point of tangent is fundamental. A point of tangent refers to a specific point on a curve where a tangent line touches the curve without crossing it. This point is crucial because it provides valuable information about the behavior of the function at that precise location. Understanding the point of tangent allows mathematicians and scientists to analyze the slope of the curve, which can indicate rates of change in various contexts such as physics, economics, and engineering.To illustrate the importance of the point of tangent, consider the example of a car moving along a curved road. At any given moment, the car's direction and speed can be represented by a tangent line to the curve of the road at the car's position. The point of tangent here would be the exact spot on the road where the tangent line best describes the car's instantaneous trajectory. By studying this point of tangent, one can determine how sharply the car must turn and how its speed may need to adjust to maintain control.Furthermore, the point of tangent is not only limited to physical applications but also extends to various fields such as economics. For instance, in analyzing cost functions, the point of tangent can reveal the marginal cost at a particular level of production. By finding the tangent line at that point of tangent, businesses can make informed decisions about pricing and output levels, optimizing their operations for maximum profit.Additionally, the point of tangent plays a significant role in optimization problems. When trying to find the maximum or minimum values of a function, one often looks for points where the derivative equals zero. These points are frequently points of tangent to the x-axis, indicating potential peaks or valleys in the function's graph. By identifying these points of tangent, one can effectively determine the optimal solutions to complex problems.In conclusion, the point of tangent is a critical concept that transcends various disciplines, offering insights into the dynamics of change and optimization. Whether in mathematics, physics, or economics, understanding the implications of a point of tangent can enhance our comprehension of complex systems and improve decision-making processes. As we continue to explore the intricacies of different fields, the significance of the point of tangent will undoubtedly remain a key element in our analytical toolkit.

在数学领域，尤其是微积分中，切点的概念是基础。切点是指曲线上的一个特定点，在这个点上，切线与曲线相接而不交叉。这个点至关重要，因为它提供了关于函数在该精确位置行为的重要信息。理解切点使得数学家和科学家能够分析曲线的斜率，这可以在物理学、经济学和工程学等各种背景下指示变化率。为了说明切点的重要性，可以考虑一个汽车沿着弯曲道路行驶的例子。在任何给定时刻，汽车的方向和速度都可以用切线来表示，切线与汽车当前位置的道路曲线相切。这里的切点将是切线最能描述汽车瞬时轨迹的确切位置。通过研究这个切点，可以确定汽车必须多么急剧地转弯，以及其速度可能需要如何调整以保持控制。此外，切点不仅限于物理应用，还扩展到经济等各个领域。例如，在分析成本函数时，切点可以揭示特定生产水平下的边际成本。通过找到该切点的切线，企业可以就定价和产出水平做出明智的决策，优化其运营以实现最大利润。此外，切点在优化问题中也扮演着重要角色。当试图找到函数的最大值或最小值时，人们常常寻找导数为零的点。这些点通常是切线与x轴相切的点，指示函数图形中的潜在峰值或谷值。通过识别这些切点，可以有效地确定复杂问题的最佳解决方案。总之，切点是一个关键概念，超越了各个学科，为变化和优化的动态提供了见解。无论是在数学、物理还是经济学中，理解切点的含义都可以增强我们对复杂系统的理解，并改善决策过程。随着我们继续探索不同领域的复杂性，切点的重要性无疑将继续成为我们分析工具箱中的关键元素。