This week we dove into section 4.6 that dealt with Related Rates. This section is similar to the set up in the previous section in 4.4, Optimization. Using the techniqes in 4.6 helps relate rate problems in calculus by solving for an equation's dervative down to the solving process.
To simplify, there are five steps to solving rate problems successfully. The first step is to draw a picture of the problem. Doing this it will help mentally inscribe what you are "actually" trying to solve. The second step involves finding a model to illustrate your picture. This is where you would come up with an equation made up of variables. You do NOT plug in the values yet, that is to come. The third step is then to find the dervative of the equation in step two. Step four, you organize all the data from the story problem. This is where you would come up with the variable you need to solve and the values for the other variables. The last and final step involves simply just plugging the values in from step 4 into step 3. Watch out, you do NOT want to plug the values back into the original equation (step two) but the dervative one (step 3).
I found this week to be a bit challenging, however a good challenge. I was able to keep up and follow each problem. Usually, I struggle with story problems. However, I am becoming more confident in dealing with them, which I believe is helping me grasp this section's concept faster.
I believe my participation went well this week. I was involved in group discussions and asked questions when needed. Next week, I am assuming we will have a chapter test. Therefore my goal is to keep working out the more difficult problems and reanalyzing the process to each story problem to do well on the test.
These websites were helpful to my understanding this week:
http://tutorial.math.lamar.edu/Classes/CalcI/RelatedRates.aspx
https://www.khanacademy.org/math/calculus/derivative_applications/rates_of_change/v/falling-ladder-related-rates
To simplify, there are five steps to solving rate problems successfully. The first step is to draw a picture of the problem. Doing this it will help mentally inscribe what you are "actually" trying to solve. The second step involves finding a model to illustrate your picture. This is where you would come up with an equation made up of variables. You do NOT plug in the values yet, that is to come. The third step is then to find the dervative of the equation in step two. Step four, you organize all the data from the story problem. This is where you would come up with the variable you need to solve and the values for the other variables. The last and final step involves simply just plugging the values in from step 4 into step 3. Watch out, you do NOT want to plug the values back into the original equation (step two) but the dervative one (step 3).
I found this week to be a bit challenging, however a good challenge. I was able to keep up and follow each problem. Usually, I struggle with story problems. However, I am becoming more confident in dealing with them, which I believe is helping me grasp this section's concept faster.
I believe my participation went well this week. I was involved in group discussions and asked questions when needed. Next week, I am assuming we will have a chapter test. Therefore my goal is to keep working out the more difficult problems and reanalyzing the process to each story problem to do well on the test.
These websites were helpful to my understanding this week:
http://tutorial.math.lamar.edu/Classes/CalcI/RelatedRates.aspx
https://www.khanacademy.org/math/calculus/derivative_applications/rates_of_change/v/falling-ladder-related-rates