Example: Rate of Change Problem
The area of a circle is increasing at a rate of . Find the rate of change of the radius when the radius is .
Example: Related Rates
A ladder 10 m long leans against a wall. The bottom slides away from the wall at 1 m/s. How fast is the top sliding down when the bottom is 6 m from the wall?
Applications
- Physics: Velocity = , Acceleration =
- Economics: Marginal cost = , Marginal revenue =
- Biology: Population growth rate =