Section 7.1 Related rates
We now study a few applications of differentiation. This is fun stuff! Our first application concerns problems involving relationships between quantities that are changing in time. Such problems are called “related rate” problems, and can usually be solved via differentiation.
Objectives
You should be able to:
- Introduce notation to express a written problem involving rates of change in terms of derivatives.
- Solve various problems from physics, chemistry, biology, etc., involving relationships between changing quantities by applying differentiation techniques (related rates problems).
Subsection 7.1.1 Instructional video
Subsection 7.1.2 Key concepts
Concept 7.1.1. Strategy to solve related problems.
- Read the problem carefully.
- Draw a picture if possible.
- Introduce notation. Assign symbols to all quantities that are functions of time.
- Express the given information and the desired rate of change in terms of derivatives.
- Write an equation that relates the various quantities of the problem. If necessary, use the geometry of the situation to eliminate one of the variables by substitution.
- Differentiate both sides of the equation with respect to \(t\text{.}\)
- Substitute the given information into the new equation and solve for the desired rate of change.
Further readings 7.1.3 Further readings
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