On Monday and Tuesday this week, we finished up our practice and review over optimization and took the quiz. Sometimes there are a few problems where it can be difficult for me to come up with the equations needed, but overall I feel pretty good about optimization.
On Wednesday we began working with related rates. I really like these kinds of problems because they are challenging and exciting when you discover the solution. The steps that we learned are very helpful to follow as well as being able to draw diagrams of the situation in each problem. I also like how they incorporate and build upon the skills that we have worked on, like implicit differentiation and writing equations relating variables. The steps for related rates are:
Step 1: Understand and Analyze
Step 2: Develop a Model
Step 3: Write an Equation Relating Variables
Step 4: Differentiate both sides implicitly with respect to t
Step 5: Substitute in known values (from step 1)
Step 6: Put the solution in context
I found these steps very helpful in finding the solutions to related rates problems but I think that I still need more practice with them. The problems that we worked through that helped me the most were the ladder sliding down the wall problem and the water level in a conical tank problem. I am able to understand these types of problems really well when we walk through them together in class, but I would like to get more comfortable with working through these problems on my own. I sometimes get stuck on understanding exactly what the question is asking and writing the equations needed to solve the problem, but I think that with more practice I will not need to look at the steps and I will get a lot better at solving related rates problems on my own.
On Wednesday we began working with related rates. I really like these kinds of problems because they are challenging and exciting when you discover the solution. The steps that we learned are very helpful to follow as well as being able to draw diagrams of the situation in each problem. I also like how they incorporate and build upon the skills that we have worked on, like implicit differentiation and writing equations relating variables. The steps for related rates are:
Step 1: Understand and Analyze
- What is going on?
- What variables are there?
- Which variables' rates of change do I know?
- Which variables' rates of change do I want to know? And under what conditions?
Step 2: Develop a Model
- Draw a picture
- Label the parts with known info
- Identify constants and label them
Step 3: Write an Equation Relating Variables
Step 4: Differentiate both sides implicitly with respect to t
Step 5: Substitute in known values (from step 1)
Step 6: Put the solution in context
- Label the solution
- Ask: Does this make sense?
I found these steps very helpful in finding the solutions to related rates problems but I think that I still need more practice with them. The problems that we worked through that helped me the most were the ladder sliding down the wall problem and the water level in a conical tank problem. I am able to understand these types of problems really well when we walk through them together in class, but I would like to get more comfortable with working through these problems on my own. I sometimes get stuck on understanding exactly what the question is asking and writing the equations needed to solve the problem, but I think that with more practice I will not need to look at the steps and I will get a lot better at solving related rates problems on my own.