What are related rates problems?

What are related rates problems?

Related rates problems are word problems where we reason about the rate of change of a quantity by using information we have about the rate of change of another quantity that’s related to it.

How do you find related rates problems?

Let’s use our Problem Solving Strategy to answer the question.

1. Draw a picture of the physical situation. See the figure.
2. Write an equation that relates the quantities of interest. A.
3. Take the derivative with respect to time of both sides of your equation. Remember the chain rule.
4. Solve for the quantity you’re after.

How do you explain related rates?

Related rates problems involve two (or more) variables that change at the same time, possibly at different rates. If we know how the variables are related, and how fast one of them is changing, then we can figure out how fast the other one is changing.

Why do we need related rates?

Related rates and problems involving related rates take advantage of quantities that are related to each other. Related rates help us determine how fast or how slow a certain quantity is changing using the rate of change of the second quantity.

How important are related rates?

Are there any other types of related rates problems?

There are still many more different kinds of related rates problems out there in the world, but the ones that we’ve worked here should give you a pretty good idea on how to at least start most of the problems that you’re liable to run into.

What are some real-life applications of related rate problems?

Solving related rate problems has many real life applications. For example, a gas tank company might want to know the rate at which a tank is filling up, or an environmentalist might be concerned with the rate at which a certain marshland is flooding. Solving the problems usually involves knowledge of geometry and algebra in addition to calculus.

What is the rate at which R1 and R2 change?

Suppose that R1 R 1 is increasing at a rate of 0.4 Ω Ω /min and R2 R 2 is decreasing at a rate of 0.7 Ω Ω /min. At what rate is R R changing when R1 = 80Ω R 1 = 80 Ω and R2 = 105Ω R 2 = 105 Ω? Okay, unlike the previous problems there really isn’t a whole lot to do here.