extremum

简明释义

英[ɪkˈstriːməm;ek-]美[ɪkˈstrɪməm]

n. [数] 极值，极端值

复 数 e x t r e m u m s 或 e x t r e m a

英英释义

单词用法

同义词

反义词

例句

1.To locate an extremum we look for these points.

为了确定极值，我们需要找这些点。

2.Spectral derivative is a simple and effective method to acquire the wavelengths of extremum points.

光谱微分方法是一种简单而有效的确定光谱曲线极值点波长位置的方法。

3.Adopting geodesics as dividing lines, space surfaces were developed by minimal extremum method.

采用测地线划分曲面，应用最小极值法进行曲面的展开。

4.A novel method for the radar full pulse data analysis, called the extremum sequence analysis method, is put forward.

针对脉冲雷达提出了一种新的雷达信号全脉冲数据分析算法？极值序列分析法。

5.This paper discusses on identification and application extension about two geometric extremum problems.

本文主要给出两个几何极值问题的证明及运用推广。

6.Through the quadratic form theory, another solution to the extremum problem of function of several variables is given.

利用二次型的理论，给出解决多元函数极值问题的另一种方法。

7.On the basis of traditional fairing algorithm, the curvature extremum of curve is used as one of the indices judging the curve fairing.

在传统光顺算法的基础上，提出了以曲线曲率极值的均方差作为衡量曲线光顺的指标之一。

8.It has revealed the relations of every extremum principle each other in certain extent.

这在一定程度上揭示了各极值原理间的相互关系。

9.In calculus, the point where a function reaches its highest or lowest value is called an extremum.

在微积分中，一个函数达到其最高或最低值的点称为极值。

10.Finding the extremum of a dataset can help identify trends and outliers.

找到数据集的极值可以帮助识别趋势和异常值。

11.The extremum of a quadratic function can be found using the vertex formula.

二次函数的极值可以通过顶点公式找到。

12.In optimization problems, we often seek to minimize or maximize an extremum.

在优化问题中，我们通常寻求最小化或最大化一个极值。

13.The extremum can be classified as either a local or global maximum or minimum.

该极值可以被分类为局部或全局最大值或最小值。

作文

In the realm of mathematics, the concept of extremum (极值) plays a crucial role in understanding the behavior of functions. An extremum can be defined as a point in a function where it reaches either a maximum or minimum value. This idea is not only fundamental in pure mathematics but also has practical applications in various fields such as economics, engineering, and even biology. Understanding how to identify and utilize extremum points can lead to more effective problem-solving and optimization strategies. To better grasp the notion of extremum, let us consider a simple quadratic function, f(x) = ax² + bx + c, where a, b, and c are constants. The shape of this function is a parabola, and depending on the value of 'a', it can open upwards or downwards. If 'a' is positive, the parabola has a minimum point, which represents the extremum of the function. Conversely, if 'a' is negative, the parabola has a maximum point, indicating the extremum. To find these points, we can use calculus by taking the derivative of the function and setting it equal to zero. This process highlights the significance of extremum in determining the optimal solutions to various problems. In real-world scenarios, the identification of extremum values can have significant implications. For instance, in economics, businesses often seek to maximize their profits or minimize costs. By analyzing their revenue functions and cost functions, they can identify the extremum points that dictate the most profitable price levels or production quantities. This application of extremum analysis is essential for making informed decisions that can lead to business success. Another area where extremum is relevant is in engineering, particularly in the design and optimization of structures. Engineers often need to determine the maximum load a bridge can support or the minimum amount of material required for a safe construction. By applying the principles of extremum analysis, they can ensure that structures are both efficient and safe, optimizing performance while minimizing costs. Moreover, in biological systems, the concept of extremum is evident in the study of population dynamics and resource allocation. For example, ecologists may explore the maximum carrying capacity of an ecosystem or the minimum resources needed for a species to thrive. Understanding these extremum points can help in conservation efforts and managing ecosystems sustainably. In conclusion, the concept of extremum (极值) is not merely an abstract mathematical idea; it is a powerful tool that finds applications across diverse fields. Whether in optimizing business strategies, engineering designs, or ecological studies, recognizing and utilizing extremum points can lead to significant advancements and improvements. As we continue to explore the world around us, the importance of extremum will undoubtedly remain at the forefront of analytical thinking and decision-making processes.

在数学领域，extremum（极值）的概念在理解函数行为方面发挥着至关重要的作用。extremum可以定义为函数中达到最大值或最小值的点。这个想法不仅在纯数学中是基础性的，而且在经济学、工程学甚至生物学等多个领域都有实际应用。理解如何识别和利用extremum点可以导致更有效的问题解决和优化策略。 为了更好地掌握extremum的概念，让我们考虑一个简单的二次函数f(x) = ax² + bx + c，其中a、b和c是常数。这个函数的形状是一个抛物线，根据'a'的值，它可以向上或向下打开。如果'a'为正，则抛物线有一个最小点，这代表了该函数的extremum。相反，如果'a'为负，则抛物线有一个最大点，表明extremum。为了找到这些点，我们可以使用微积分，通过对函数求导并将其设置为零来实现。这个过程突显了extremum在确定各种问题的最佳解决方案中的重要性。 在现实世界场景中，识别extremum值可能具有重要的意义。例如，在经济学中，企业通常寻求最大化利润或最小化成本。通过分析他们的收入函数和成本函数，他们可以识别出决定最盈利价格水平或生产数量的extremum点。这种extremum分析的应用对于做出明智的决策以实现商业成功至关重要。 extremum在工程学中也是相关的，特别是在结构设计和优化方面。工程师通常需要确定桥梁能够承受的最大负载或安全施工所需的最小材料量。通过应用extremum分析的原则，他们可以确保结构既高效又安全，同时优化性能并降低成本。 此外，在生物系统中，extremum的概念在种群动态和资源分配的研究中显而易见。例如，生态学家可能会探索生态系统的最大承载能力或某个物种生存所需的最小资源。理解这些extremum点可以帮助保护工作和可持续管理生态系统。 总之，extremum（极值）的概念不仅仅是一个抽象的数学思想；它是一个强大的工具，在不同领域中得到了应用。无论是在优化商业策略、工程设计还是生态研究中，识别和利用extremum点都可以带来显著的进步和改善。随着我们继续探索周围的世界，extremum的重要性无疑将在分析思维和决策过程中保持在前沿。