Applications of Derivatives · Theorems
Related Rates
Related rates problems involve finding how fast one quantity changes given how fast another changes. Differentiate an equation relating the quantities with respect to time.
- 0 variables
- 2 worked examples
- 15 in Applications of Derivatives
Worked examples
A circle has radius growing at 2 cm/s. Find dA/dt when r = 5 cm.
- A = πr². Differentiate: dA/dt = 2πr · dr/dt
- dA/dt = 2π(5)(2) = 20π
Answer: dA/dt = 20π ≈ 62.83 cm²/s
1 more worked examplePremium
A 10-ft ladder slides down a wall. The base moves at 1 ft/s. How fast does the top slide when the base is 6 ft from the wall?
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Practice
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