This week was somewhat of a re-cap in AP Calculus towards the beginning when we started off reviewing and gaining a better understanding of optimization problems and how to solve them. We took a quiz over optimization, and as far as I can tell, it seemed to have gone pretty good. For the most part, I understood what I was being asked in the quiz questions and I knew how to find the answers.
Just as a re-cap of solving optimization problems, the steps I use are as follows:
#1 - Understand what you are being asked to find and assess what you have been given.
#2 - Develop a model for the variable you are trying to find using basic algebra.
#3 - Develop an equation relating two variables using basic algebra and given information.
#4 - Create a diagram to better illustrate the variables and constants in the problem.
#5 - Solve the relating equation for one of the variables.
#6 - Substitute this variable into the model that was developed.
#7 - Take the derivative of this newly written equation.
#8 - Algebraically, set this equal to zero and solve for a variable. Graphically, identify the zeroes of the function.
#9 - Connect your solution back to the problem!
Learning how to complete problems concerning related rates was a bit more difficult conceptually, but after developing a strategy I could use to find a solution, these types of problems became much simpler.
The process I use to solve related rates problems is very similar to the way I would solve a regular optimization problem. However, now I must take into consideration the presence of changing variables. Related rates problems are asking for precisely that, rates, which means finding the answer will be much more complex and entails more work.
Essentially, the process I use when solving related rates problems is:
#1 - Understand what you are being asked to find and assess what you have been given.
#2 - Create a chart with three columns reading: "Constant", "Changing", and "Conditions" where you can list and keep organized the constants, changing variables, and conditions given.
#3 - Create a diagram to better illustrate the variables and constants in the problem.
#4 - Develop an equation relating the changing variables using algebra and constants.
#5 - Develop a model for the variable you are trying to find using basic algebra.
#6 - Solve the relating equation for one of the variables.
#7 - Substitute this variable into the model that was developed.
#8 - Implicitly derive the equation since you are trying to find rate.
#9 - Substitute given information and conditions into the implicitly derived equation.
#10 - Solve the problem and connect your solution back to the problem!
Success in solving these types of problems really comes down to staying organized and really understanding what is being asked of you. Connecting your solution to the original question is crucial because it can help determine whether or not you have solved it correctly. The answer to the problem should be logical when it is reapplied to the original problem.
Just as a re-cap of solving optimization problems, the steps I use are as follows:
#1 - Understand what you are being asked to find and assess what you have been given.
#2 - Develop a model for the variable you are trying to find using basic algebra.
#3 - Develop an equation relating two variables using basic algebra and given information.
#4 - Create a diagram to better illustrate the variables and constants in the problem.
#5 - Solve the relating equation for one of the variables.
#6 - Substitute this variable into the model that was developed.
#7 - Take the derivative of this newly written equation.
#8 - Algebraically, set this equal to zero and solve for a variable. Graphically, identify the zeroes of the function.
#9 - Connect your solution back to the problem!
Learning how to complete problems concerning related rates was a bit more difficult conceptually, but after developing a strategy I could use to find a solution, these types of problems became much simpler.
The process I use to solve related rates problems is very similar to the way I would solve a regular optimization problem. However, now I must take into consideration the presence of changing variables. Related rates problems are asking for precisely that, rates, which means finding the answer will be much more complex and entails more work.
Essentially, the process I use when solving related rates problems is:
#1 - Understand what you are being asked to find and assess what you have been given.
#2 - Create a chart with three columns reading: "Constant", "Changing", and "Conditions" where you can list and keep organized the constants, changing variables, and conditions given.
#3 - Create a diagram to better illustrate the variables and constants in the problem.
#4 - Develop an equation relating the changing variables using algebra and constants.
#5 - Develop a model for the variable you are trying to find using basic algebra.
#6 - Solve the relating equation for one of the variables.
#7 - Substitute this variable into the model that was developed.
#8 - Implicitly derive the equation since you are trying to find rate.
#9 - Substitute given information and conditions into the implicitly derived equation.
#10 - Solve the problem and connect your solution back to the problem!
Success in solving these types of problems really comes down to staying organized and really understanding what is being asked of you. Connecting your solution to the original question is crucial because it can help determine whether or not you have solved it correctly. The answer to the problem should be logical when it is reapplied to the original problem.