Name: brook trout growth vs water temperature
Uploaded: 2026-07-24T11:46:38.212Z
Duration: 1 min 26 s
Channel: JoVE

假设水温影响了溪鳟的生长速率。在不同水温下，其在固定时间段内增加的体重已被记录成表。通过使用导数来估计生长速率对温度变化的响应。在第一个数据点处，使用前向割线的斜率来近似导数 在第一点与第二点之间绘制的线。在第二个点处，通过计算连接前一个点和后一个点的割线斜率，使用中心差分法估算导数，从而获得更精确的导数估计值。在第三个点处，再次使用中心差分法计算连接其前后两点的割线斜率。同样，在第四个点处，导数是利用相邻数据点之间割线的斜率来计算的。最后，在最后一个点处，通过绘制最后两个数据点之间的后向割线，利用其斜率来近似该点的导数。这些导数估计值汇总在一张表格中。相应的图表显示出生长速率呈持续下降趋势，表明温度与体重增加之间存在负相关关系。

变化率：问题求解

Rate of Change: Problem Solving

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Education

教育

JoVE Core

Calculus

微积分

Unit

单元

Derivatives

导数

KEY TERMS AND CONCEPTS

关键术语与概念

brook trout growth vs water temperature

Brook trout growth changes with water temperature. The data show how trout weight shifts over a 24-day period at several temperatures. At cooler water temperatures, such as 15.5 degrees Celsius, the trout gain a lot of weight. As the temperature rises, the amount of weight gained gets smaller.

At the warmest temperature tested, 24.4 degrees Celsius, the trout have a net loss in weight. This pattern suggests that brook trout do better in cooler water. Warmer water may create metabolic stress or reduce growth efficiency.

The rate of change in weight is estimated by comparing nearby temperature values. Rate of change means how much the trout's weight changes for each degree Celsius. When only one nearby point is available, the estimate uses the change between those two points. When a point lies between two others, the two nearby rates are averaged to get a better estimate.

These estimates show that the growth rate becomes more negative as temperature increases. That means the trout grow less efficiently and may begin losing weight in warmer water. A graph of the rates shows a steady decline. The overall trend supports the conclusion that higher water temperatures are less favorable for brook trout growth.

Brook Trout Growth vs Water Temperature

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rate of change: problem solving

Brook trout growth changes with water temperature. The data show how trout weight shifts over a 24-day period at several temperatures. At cooler water temperatures, such as 15.5 degrees Celsius, the trout gain a lot of weight. As the temperature rises, the amount of weight gained gets smaller. At the warmest temperature tested, 24.4 degrees Celsius, the trout have a net loss in weight. This pattern suggests that brook trout do better in cooler water. Warmer water may create metabolic stress or...

key terms and concepts

See how brook trout weight changes with water temperature and how rate of change helps show why cooler water supports better growth.

Brook Trout Growth vs Water Temperature | JoVE K12

The JoVE Core Calculus collection provides a comprehensive visual guide to the entire calculus sequence, seamlessly connecting mathematical theory to real-world applications in physics and economics. Through dynamic animated lessons, the course transitions smoothly from foundational single-variable concepts to advanced multivariable topics. Students will explore everything from standard differentiation and integration to spatial vectors, multi-dimensional derivatives, and complex vector fields. By breaking down abstract coordinate systems, infinite series, and spatial motion, this structured approach builds the robust analytical skills and advanced mastery essential for STEM success.

calculus

Brook Trout Growth vs Water Temperature

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