Hey guys we are almost done!! We just took our last test of the semester and now the only thing we have is the final!! Whoooo!! We are so close! We need to not get lazy and keep up the hard work so we can pass this class with ease! I looked ahead and noticed that we are about to learn about related rates in class, so I thought I would give everyone a little insight on what to expect on the next lesson. This lesson should be fairly easy because we are just using information we already know and just adding a little extra twist in it. In these types of problems we will be given a rate of change associated with one value and then be given another rate of change related to a second value. The second value will also be related to the first value. It seems tricky, but it is really not that bad once we perform examples in class. These problems are very similar to our optimization problems because we will have to figure out what equation we will need that includes both rates of change. When making the equation we will also have to pair up the right rate of change with the right value. These problems take a lot of because starting the problem and making the right equation is key to success.
Once you find the equations that associates the rates of change correctly, we will use the familiar chain rule to find the derivative of the equation. We will then be able to find the differentials of the equation. We can also use the differential approximation to different rates of changes of variables, if the rate of change is not given for a certain value.
I found some helpful strategies on the internet that might help you, when approaching these types of problems:
- Draw a diagram. This is the most helpful step in related rates problems. It allows us to visualize the problem.
- Assign variables to each quantity in the problem that is a function of time. Each of these values will have some rate of change over time.
- List all information that is given in the problem and the rate of change that we are trying to find.
- Write an equation that associates the variables with one another. If there are variables for which we are not given the rates of change (except for the rate of change that we are trying to determine), we must find some relation form the nature of the question that allows us to write these variables in terms of variables for which the rates of change are given. We mist then substitute these relations into the main equation.
- Using the chain rule, differentiate each side of the equation with respect to time
- Substitute all given information into the equation and solve for the required rate of change.
Like I said earlier, rates of change problems are really easy. The hardest part is getting starting and organizing your information. No need to worry! :]