Difference Between Related Rates And Optimization Problems

Distinct Differences from Related Rates. As you have already learned, related rates problems allow us to determine the change in one variable as a certain set of requirements are changing. In contrast, within optimization problems, the variables are fixed. In an optimization problem we do not need to determine the rate at which variables are

a genuine attempt at solving the problem, which may be either computational, or a discussion of ideas or concepts you believe may be in play, For high school calculus, there aren't that many types of optimization and related rates questions. The more you do, the easier it becomes to recognize what kind of problem it is and how to approach

This section contains lecture video excerpts, lecture notes, two problem solving videos, and a worked example on related rates. Optimization, Related Rates and Newton's Method Session 31 Related Rates Session 31 Related Rates Course Home

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.

In addition to optimization, this part of the course also describes how to use derivatives to relate two rates of change and to estimate the values for which a function's output is zero. Session 29 Optimization Problems Session 30 Optimization Problems II Session 31 Related Rates

The derivative, dvdt would be the rate of change of v. When solving related rates problems, we should follow the steps listed below. 1 Draw a diagram. This is the most helpful step in related rates problems. It allows us to visualize the problem. 2 Assign variables to each quantitiy in the problem that is a function of time.

Even though this looks like a related rates problem, its actually optimization, where we use what we know about the relationship between time and velocity dvt t d v. So we know the distance we run is x feet, and we can run at a rate of 15 feetsecond. It takes us this much time t x x 15. We know the distance we have to swim by Pythag y 2

optimization equation in order to obtain an equation with just one independent variable. Specific advice for related rates problems -- A figure tends to give a fixed, static impression, but keep in mind that these problems involve dynamic situations. Picture in your mind how things are changing with time--the term variable

L13 Related Rates and Optimization Related rates allow us to nd the rate of change of one quantity in terms of the rate of change of a related quantity. To solve a related rates problem 1. Identify the desired rate of change assign variables to all related quantities. Determine what rates are given at a particular instant in time and

4.8 Optimization 4.9 More Optimization Problems For these related rates problems, it's usually best to just jump right into some problems and see how they work. The only real difference between them was coming up with the relationship between the known and unknown quantities. This is often the hardest part of the problem.