Rates of Change and Related Rates
This lesson covers rates of change and related rates using examples in different contexts such as temperature, area, velocity, population growth, and electrical circuits. The derivative is introduced as the instantaneous rate of change, and related rates problems are solved using implicit differentiation and the chain rule. The lesson also includes a demonstration of how to find the rate at which a spotlight moves past a point on the shoreline, and the rate at which a tank with a cone shape fills up with water.
The derivative as rate of change. Related rates problems.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
- The Derivative as a Rate of Change - Practice with The Derivative as a Rate of Change.
- Rates of Change Per Unit Time - Practice with Rates of Change Per Unit Time.
- What is a rate of change?
- How is a derivative a rate of change?
- Why is current the rate of change of charge?
- What is dV/dt for the volume of a cylinder?
- How do you solve a Calculus problem with a cone-shaped water tank being filled with water?
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Staff Review
This video represents the derivative as a rate of change. Some real-life situations are explained with their units, the dependent / independent variable, and the rate of change in the situation. A ball dropping situation is used as an example of velocity being the derivative of the height function. An example of a pond being stocked with fish is also used to explain rate of change. Several more examples, including a couple of classic Calculus problems, are explained well in this video. -
Dee101
This video handles rates of change and related rates excellently. The presentation is clear and the choice of examples used demonstrates the concepts very well. Excellent Job!!! -
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