critical number

简明释义

临界数

英英释义

例句

1.In order to achieve the project goals, we need to identify the critical number 关键数字 of resources required.

为了实现项目目标，我们需要确定所需资源的关键数字。

2.For the experiment to be valid, we must ensure that the sample size meets the critical number 关键数字 of participants.

为了实验的有效性，我们必须确保样本量达到所需的关键数字参与者数量。

3.The critical number 关键数字 of sales needed this quarter is significantly higher than last year.

本季度所需的关键数字销售额远高于去年。

4.During the meeting, we discussed the critical number 关键数字 of customers we need to retain to stay profitable.

在会议中，我们讨论了保持盈利所需的关键数字客户数量。

5.The critical number 关键数字 of points needed to qualify for the finals is 300.

晋级决赛所需的关键数字积分是300分。

作文

In the world of mathematics and science, the term critical number refers to a specific value at which a function's behavior changes. This concept is essential for understanding various phenomena, including optimization problems and the analysis of functions. For instance, when we are trying to find the maximum or minimum values of a function, we often look for its critical number. These numbers are derived from the function's derivative, which helps us determine where the slope of the function is zero or undefined. To illustrate, consider a simple quadratic function such as f(x) = -2x² + 4x + 1. To find the critical number, we first need to compute the derivative of the function. The derivative, f'(x), gives us the rate of change of the function at any point x. For our function, f'(x) = -4x + 4. Setting this equal to zero allows us to solve for x: -4x + 4 = 0 -4x = -4 x = 1. Thus, x = 1 is a critical number. This means that at x = 1, the function changes its direction, indicating a local maximum or minimum. By evaluating the second derivative or using the first derivative test, we can confirm whether this critical number corresponds to a maximum or minimum value of the function. Understanding critical numbers is not limited to pure mathematics; it has practical applications in various fields such as economics, engineering, and physics. For example, in economics, businesses often need to determine the optimal production level to maximize profit. By identifying the critical number of units produced where marginal cost equals marginal revenue, companies can make informed decisions about their operations. Moreover, in physics, the concept of critical number plays a significant role in analyzing motion. When studying the trajectory of a projectile, scientists can use critical numbers to determine the points at which the projectile reaches its highest altitude or the point of impact. This information is crucial for engineers designing structures or vehicles that must withstand certain forces. In conclusion, the term critical number encapsulates a fundamental idea in mathematics that transcends into real-world applications. Whether it is optimizing a business strategy or analyzing physical systems, recognizing and understanding critical numbers is vital for making informed decisions. As we delve deeper into various fields of study, the importance of these numbers becomes increasingly evident, highlighting the interconnectedness of mathematics with the world around us. Therefore, mastering the concept of critical numbers is essential for anyone looking to excel in analytical disciplines.

在数学和科学的世界里，术语临界数指的是一个特定的值，在这个值上，函数的行为发生变化。这个概念对于理解各种现象至关重要，包括优化问题和函数分析。例如，当我们试图找到一个函数的最大值或最小值时，我们通常会寻找它的临界数。这些数字是从函数的导数中得出的，帮助我们确定函数的斜率在哪些地方为零或未定义。为了说明这一点，考虑一个简单的二次函数，比如f(x) = -2x² + 4x + 1。要找到临界数，我们首先需要计算该函数的导数。导数f'(x)给我们提供了函数在任何点x的变化率。对于我们的函数，f'(x) = -4x + 4。将其设为零可以让我们求解x：-4x + 4 = 0-4x = -4x = 1。因此，x = 1是一个临界数。这意味着在x = 1时，函数改变了方向，指示着局部最大值或最小值。通过评估第二导数或使用第一导数测试，我们可以确认这个临界数是否对应于函数的最大值或最小值。理解临界数不仅限于纯数学；它在经济学、工程学和物理学等多个领域都有实际应用。例如，在经济学中，企业常常需要确定最佳生产水平以最大化利润。通过识别生产单位的临界数，即边际成本等于边际收益的点，公司可以做出明智的运营决策。此外，在物理学中，临界数的概念在分析运动时也发挥着重要作用。当研究抛射物的轨迹时，科学家可以使用临界数来确定抛射物达到最高高度或撞击点的时刻。这些信息对于设计必须承受特定力的结构或车辆的工程师至关重要。总之，术语临界数概括了数学中的一个基本思想，这一思想超越了现实世界的应用。无论是优化商业策略还是分析物理系统，识别和理解临界数对于做出明智的决策至关重要。随着我们深入研究各个学科，这些数字的重要性变得越来越明显，突显了数学与我们周围世界之间的相互联系。因此，掌握临界数的概念对于任何希望在分析学科中出类拔萃的人来说都是至关重要的。