This week we dove into section 4.4 that dealt with optimization. This consisted of various topics of story problems that were all associated with finding derivatives to solve them. In other terms, everything I have learned about the process of derivatives was used to solve equations used in complicated geometry, algebra, trigonometry, ect.
At first I struggled with the story problems. However as the week went on, with more practice I became a lot more confident and started to grasps the concepts better. I understood when to find the maximum or minimum capacity of an object fairly well. The process in solving for these equations is to find an equation in where you are able to substitute one variable out to plug in to the second equation. When you do this you are now only left with one variable. From this you are able to solve the equation right away by graphing the function and finding its min or max point. If you want to challenge your mathematical skills you can also find the answer by solving for the function's derivative to interpret its zeros. From knowledge of the previous trimester you know that zeros of the derivative are the max/min of the function. To find which point is the max and which one is the min you do the testing method of increasing vs. decreasing of the number line to figure it out.
I believe my participation this week was well. I enjoyed going over the story problems one by one from the assignment in those two days. I found this strategy to be helpful, and it really allowed me to understand the methods behind each story problem. I need to continue working on my basic algebra skills to help with simplifying my answers by hand when solving complicated problems. Next week, I am assuming we will continue working in chapter 4 and find new techniques and strategies in analyzing and solving graphs using derivative properties.
These links I found helpful with this section: http://tutorial.math.lamar.edu/Classes/CalcI/Optimization.aspx
https://www.khanacademy.org/math/calculus/derivative_applications
At first I struggled with the story problems. However as the week went on, with more practice I became a lot more confident and started to grasps the concepts better. I understood when to find the maximum or minimum capacity of an object fairly well. The process in solving for these equations is to find an equation in where you are able to substitute one variable out to plug in to the second equation. When you do this you are now only left with one variable. From this you are able to solve the equation right away by graphing the function and finding its min or max point. If you want to challenge your mathematical skills you can also find the answer by solving for the function's derivative to interpret its zeros. From knowledge of the previous trimester you know that zeros of the derivative are the max/min of the function. To find which point is the max and which one is the min you do the testing method of increasing vs. decreasing of the number line to figure it out.
I believe my participation this week was well. I enjoyed going over the story problems one by one from the assignment in those two days. I found this strategy to be helpful, and it really allowed me to understand the methods behind each story problem. I need to continue working on my basic algebra skills to help with simplifying my answers by hand when solving complicated problems. Next week, I am assuming we will continue working in chapter 4 and find new techniques and strategies in analyzing and solving graphs using derivative properties.
These links I found helpful with this section: http://tutorial.math.lamar.edu/Classes/CalcI/Optimization.aspx
https://www.khanacademy.org/math/calculus/derivative_applications