I initially thought that height was the Y value of the right triangle but the visualization and your explanation clarified that the height is referring to the Y + X. Also, one thing I liked about the video was your use of the second derivative to determine max rather than testing out numbers to left and right of 1 on the first derivative test. NA MAC 2311.
Krystal Silva MAC2311 One new concept I learned from this video was is how you explained the problem in terms of x and y. at 3:48 made me realized why I kept struggling with problems like this.
Sharon S Mac 2311 The video helped me understand while solving these problems can take time, using different terms like x and y can make it easier. It highlighted the importance of breaking functions into primary and secondary equations and checking from both perspectives. Overall, it demonstrated that with practice, figuring out equations in one variable becomes simpler.
Lydia F. MAC2311 The video helped me review volumes and I also gained an understanding of finding the critical values which I have had trouble grasping. I found how to verify my answer very helpful aswell.
johana sepulveda mac2311 personally learning how to use the common factor to then find derivative was a game change for me. this type of problems freaked me out, but its not as bad as i thought, the break down of this entire problem really made the difference.
Guyptamah G. MAC2311 When first saw this problem I was trying to figure out the best way to solve it. After I watched it, I realized that I just need to learn the steps you take to solve it. because I already knew some of the steps such as how to find the derivative of a function, the volume of a right circular cone etc… for the rest I just need to apply what I already know using the right steps. thank you for making learning easier for us.❤️
Mario Piacquadio MAC2311 One thing I liked about the video was how all of the aspects of mathematics we have learned until this point are coming together here, some aspects of trigonometry, as well as a lot of things we have learned so far in calculus.
Melissa Gardiner MAC2311 One takeaway from this video was learning how to factor correctly when you were at the second step of finding the derivative. When a problem has a lot written in it, I get overwhelmed and tend to make small mistakes so I appreciated how you showed how you got from each step.
Heidy Carralero MAC2311 The video helped me understand that using primary and secondary equations are important because they help break up a function. I also learned that when I optimize a function I may have to look at it in both terms of x and y to see which can be easier to solve.
Lauren Pinder MAC2311 The video helped me understand that when maximizing the volume you need to write the primary equation and include information given in the problem so that you have x in terms of y or y in terms of x.
MAC2311 This video helped me understand how to do the second equation and solve it in terms of y. Also, I learned how to get the second derivative and the maximum.
ramón de la paz Mac2311 A new concept I learned from this video was that the first thing we should do in a optimization problem is to identify the quantity that is being maximize or minimize.
Fabrizio Hidalgo MAC2311 The video helped me understand better how to relate calculus to real-world measurements. It's a tough concept to grasp when you don't have all the details, but this helps greatly.
David B. MAC2311 One key takeaway that I had from this video is that you need to stay flexible when solving problems like these and really understand what the objective is. In order to get the volume, unless you really understand what the problem is you won't know how to adapt the primary equation to fit the problem.
Michael Adams MAC2311 The video helped me understand that values less than zero during the 2nd derivative test are a maximum, while values greater than zero are a minimum
Jonathan Morency MAC2311 One take-away from this video is that solving problems like this do take a long time, but being able to write it in different terms of either x and y can make the process easier.
Alexis C. MAC2311 One take-away from this video is that the Pythagorean Theorem can be used as a second equation in order to find the function of one variable.
Michael Bryan Mac2311 From this video I learned the formulas we learned for algebra, trig, and geometry all intertwine and are often used in a combination in CALC.
Luis Acosta MAC2311 The video helped me realize the importance of using primary and secondary equations to break down a function. I also learned that when optimizing a function, it can be helpful to consider it in terms of both x and y to determine which variable makes the solution easier
Mateo Gelman MAC2311 One takeaway I had was how important it is to stay organized especially when doing something that has a primary and secondary equations.
Ashley M. MAC2311 One take-away from this video is that the formulas I've learned from geometry, algebra, and trigonometry are all utilized in the problems shown in this video.
Adam Minieri MAC2311 An insight I gained from watching this video was that when we solve for the derivative with respect to y we can factor out common factors to get the critical values more conveniently.
Sebastian Torres MAC2311 One take-away from this video is the importance of choosing a simple function to differentiate when optimizing. That way it can make the process easier which makes it harder to make silly mistakes.
Gisela Pacheco MAC2311 I'm not the best at this type of problems but watching the video help me achieve a better understanding of it also the fact we can use common factor to get critical values makes it ten times easier
Maria Leon MAC2311 The video helped me understand how to utilize the common factor when solving the derivative to be more efficient when solving the problem.
kaithlyn Pierre-Louis MAC2311 my take away from this video is that this is a long process but if you take your time you are able to find easier ways to solve this problem like how you were able to factor out 9-y^2 to 3+y and 3-y and by doing that you were able to have a immediate factored form.
Jairo Hillon MAC2311 This video is very useful to understand the critical thinking process that is necessary to find, relate, and use the primary and secondary equations. Although every exercise requires a different formulas, after reviewing many exercises it become easier to figure out how to build the equation in terms of only one variable.
Francisco Juarez MAC2311 I found this video extremely satisfying since I was struggling with this problem in my math labs the other day, this video taught me how to solve it, I had no idea we had the Pythagorean theorem.
Yusra Jabeen MAC2311 One new concept I learned from this video was when writing your equations you're solving for one variable so there should be only all X or all Y present.
Jesus Perez MAC2311 One new concept I learned from this video was one i reviewed the volume of a cone along with the pythagorean theorem and with that information we can get the function of one variable.
Danielle Sanchez MAC2311 I learned from this video that simplifying a function into a polynomial, if possible, makes for a more effecient way to solve for a derivative.
Jonathan Amador MAC2311 An insight I gained from watching this video was to step by step factor eliminate common factors so as not to get confused with other variables in the equation.
jennifer clark mac2311 an insight i gained that was helpful was the fact that we can factor out common factors when solving derivatives to get your critical values easier
I initially thought that height was the Y value of the right triangle but the visualization and your explanation clarified that the height is referring to the Y + X. Also, one thing I liked about the video was your use of the second derivative to determine max rather than testing out numbers to left and right of 1 on the first derivative test. NA MAC 2311.
Krystal Silva
MAC2311
One new concept I learned from this video was is how you explained the problem in terms of x and y. at 3:48 made me realized why I kept struggling with problems like this.
Sharon S
Mac 2311
The video helped me understand while solving these problems can take time, using different terms like x and y can make it easier. It highlighted the importance of breaking functions into primary and secondary equations and checking from both perspectives. Overall, it demonstrated that with practice, figuring out equations in one variable becomes simpler.
Lydia F.
MAC2311
The video helped me review volumes and I also gained an understanding of finding the critical values which I have had trouble grasping. I found how to verify my answer very helpful aswell.
Correct answer .Thank you
johana sepulveda
mac2311
personally learning how to use the common factor to then find derivative was a game change for me. this type of problems freaked me out, but its not as bad as i thought, the break down of this entire problem really made the difference.
Great to hear!
Guyptamah G.
MAC2311
When first saw this problem I was trying to figure out the best way to solve it. After I watched it, I realized that I just need to learn the steps you take to solve it. because I already knew some of the steps such as how to find the derivative of a function, the volume of a right circular cone etc… for the rest I just need to apply what I already know using the right steps. thank you for making learning easier for us.❤️
Mario Piacquadio
MAC2311
One thing I liked about the video was how all of the aspects of mathematics we have learned until this point are coming together here, some aspects of trigonometry, as well as a lot of things we have learned so far in calculus.
Melissa Gardiner
MAC2311
One takeaway from this video was learning how to factor correctly when you were at the second step of finding the derivative. When a problem has a lot written in it, I get overwhelmed and tend to make small mistakes so I appreciated how you showed how you got from each step.
Heidy Carralero
MAC2311
The video helped me understand that using primary and secondary equations are important because they help break up a function. I also learned that when I optimize a function I may have to look at it in both terms of x and y to see which can be easier to solve.
Lauren Pinder
MAC2311
The video helped me understand that when maximizing the volume you need to write the primary equation and include information given in the problem so that you have x in terms of y or y in terms of x.
MAC2311
This video helped me understand how to do the second equation and solve it in terms of y. Also, I learned how to get the second derivative and the maximum.
I take time to solve some complex questions more than required how to improve it
ramón de la paz
Mac2311
A new concept I learned from this video was that the first thing we should do in a optimization problem is to identify the quantity that is being maximize or minimize.
Fabrizio Hidalgo
MAC2311
The video helped me understand better how to relate calculus to real-world measurements. It's a tough concept to grasp when you don't have all the details, but this helps greatly.
David B.
MAC2311
One key takeaway that I had from this video is that you need to stay flexible when solving problems like these and really understand what the objective is. In order to get the volume, unless you really understand what the problem is you won't know how to adapt the primary equation to fit the problem.
Joshua Brunk
MAC2311
I liked how you showed rules of geometry and calculus together combining the two mathematics.
Michael Adams
MAC2311
The video helped me understand that values less than zero during the 2nd derivative test are a maximum, while values greater than zero are a minimum
Annabel Valdes
MAC 2311
A new concept I learned from this video was Optimization and how to solve a problem in one of the easiest ways.
Thanks for posting!
Jonathan Morency
MAC2311
One take-away from this video is that solving problems like this do take a long time, but being able to write it in different terms of either x and y can make the process easier.
Alexis C.
MAC2311
One take-away from this video is that the Pythagorean Theorem can be used as a second equation in order to find the function of one variable.
Michael Bryan
Mac2311
From this video I learned the formulas we learned for algebra, trig, and geometry all intertwine and are often used in a combination in CALC.
So true!
Asia Jones
MAC2311 ( Summer 2024)
I learned how to formulate my equations and how to substitute the accurate data to get the correct results.
Luis Acosta
MAC2311
The video helped me realize the importance of using primary and secondary equations to break down a function. I also learned that when optimizing a function, it can be helpful to consider it in terms of both x and y to determine which variable makes the solution easier
Mateo Gelman
MAC2311
One takeaway I had was how important it is to stay organized especially when doing something that has a primary and secondary equations.
Ashley M.
MAC2311
One take-away from this video is that the formulas I've learned from geometry, algebra, and trigonometry are all utilized in the problems shown in this video.
Adam Minieri
MAC2311
An insight I gained from watching this video was that when we solve for the derivative with respect to y we can factor out common factors to get the critical values more conveniently.
Very useful tool!
Sebastian Torres
MAC2311
One take-away from this video is the importance of choosing a simple function to differentiate when optimizing. That way it can make the process easier which makes it harder to make silly mistakes.
Gisela Pacheco
MAC2311
I'm not the best at this type of problems but watching the video help me achieve a better understanding of it also the fact we can use common factor to get critical values makes it ten times easier
Give it time and practice and you will be great! Thanks for sharing.
Caroline Anderson
MAC2311
One thing I liked about this video was that there were different methods to achieve the same answer.
Maria Leon
MAC2311
The video helped me understand how to utilize the common factor when solving the derivative to be more efficient when solving the problem.
kaithlyn Pierre-Louis
MAC2311
my take away from this video is that this is a long process but if you take your time you are able to find easier ways to solve this problem like how you were able to factor out 9-y^2 to 3+y and 3-y and by doing that you were able to have a immediate factored form.
Jairo Hillon
MAC2311
This video is very useful to understand the critical thinking process that is necessary to find, relate, and use the primary and secondary equations. Although every exercise requires a different formulas, after reviewing many exercises it become easier to figure out how to build the equation in terms of only one variable.
Francisco Juarez MAC2311
I found this video extremely satisfying since I was struggling with this problem in my math labs the other day, this video taught me how to solve it, I had no idea we had the Pythagorean theorem.
Yusra Jabeen
MAC2311
One new concept I learned from this video was when writing your equations you're solving for one variable so there should be only all X or all Y present.
Ayasha Hudson
MAC2311
One thing I liked about this video was the thorough explanation.
I'm so glad!
Amy-Nicole Toro
MAC2311
One new conept i learned was how to take derivatives with pie. Great video, thank you!
Glad it was helpful!
Gianna Brito
MAC2311
One new concept that I found helpful was utilizing the common factor when solving the derivative in order to be more efficient.
Jesus Perez
MAC2311
One new concept I learned from this video was one i reviewed the volume of a cone along with the pythagorean theorem and with that information we can get the function of one variable.
Danielle Sanchez
MAC2311
I learned from this video that simplifying a function into a polynomial, if possible, makes for a more effecient way to solve for a derivative.
Jonathan Amador
MAC2311
An insight I gained from watching this video was to step by step factor eliminate common factors so as not to get confused with other variables in the equation.
Isaiah Belvant
MAC 2311
One take away from this video identifying the amount being maximized and minimized. As well as taking derivatives with pie.
Steven Brown
MAC2311
An insight I gained from watching this video was that potential critical points had to be positive or reasonable.
Lilian Garcia MAC2311 One new concept that I found helpful was utilizing the common factor when solving the derivative as this is more efficient.
jennifer clark
mac2311
an insight i gained that was helpful was the fact that we can factor out common factors when solving derivatives to get your critical values easier