Related rates problems are ones that talk about the rate at which something changes in relation to something else. In other words, one variable is changing because another variable is changing. Some tips on setting up your related rates problem:
- Draw a picture of the scenario.
- ONLY label things that are constant.
- Use variables for the things that are not constant.
- Set up equations relating the two variables (get one variable in terms of the other).
- Differentiate with respect to time.
- Substitute back in all known values. Sometimes you may have to manipulate your equations to find these ‘known’ values.
Don’t forget that both ‘x’ and ‘y’ are independent functions in this scenario, and so when you take the derivative of the equation, you must remember to use the chain rule.
Here's another example: Imagine your roof is leaking, and theres a singular drip coming into your living room. It’s creating a pud- dle in the middle of your floor, and the radius of the puddle is increasing at a rate of 8 cm/s. How fast is the area of the the puddle increasing when the radius gets to 100 cm?
Here's another example: Imagine your roof is leaking, and theres a singular drip coming into your living room. It’s creating a pud- dle in the middle of your floor, and the radius of the puddle is increasing at a rate of 8 cm/s. How fast is the area of the the puddle increasing when the radius gets to 100 cm?