This week we kind of reviewed more related rates problems (more challenging ones) in preparation for our quiz we took on Monday. The problems that I struggled with the most I think are the problems in which I have to solve for another variable and then substitute it before deriving the model. I only find this challenging because I tend to solve for whichever variable will help me the least to solve the problem. And so, it gets extremely messy when I begin to derive especially if I have to do the chain rule within the product rule within the quotient rule to solve for my rate. However, I am getting better at it, I just have to go slowly and make sure I am substituting the proper variable in order to solve for my rate and it becomes much easier and less messy to derive my model.
The question I found very difficult was the question on the test pertaining to the conical cup. I knew what model I needed and the proper number to plug in before solving for my derivative. I also knew how to solve for the variables I was not given by using similar triangles. I think I messed up because I solved the derivative of the similar triangles equation I made in order to get dh/dt and dx/dt because I thought then I could solve for dh/dt and plug that into my derivative equation for dx/dt since I was solving for dh/dt, but I don't think I could do that. I also may have messed up somewhere in finding my derivative because it was so messy that there was a lot of room for error.
Other than the one complicated question on the quiz, I found the quiz to go pretty well. The last question on the quiz basically regarded solving for dy after implicitly deriving a function with a given x and a given dx. I found this to be pretty easy and very helpful when I am doing really in depth related rates problems because it is sometimes very hard to remember that you can break up dy and dx into two separate variables.
See the video!
The question I found very difficult was the question on the test pertaining to the conical cup. I knew what model I needed and the proper number to plug in before solving for my derivative. I also knew how to solve for the variables I was not given by using similar triangles. I think I messed up because I solved the derivative of the similar triangles equation I made in order to get dh/dt and dx/dt because I thought then I could solve for dh/dt and plug that into my derivative equation for dx/dt since I was solving for dh/dt, but I don't think I could do that. I also may have messed up somewhere in finding my derivative because it was so messy that there was a lot of room for error.
Other than the one complicated question on the quiz, I found the quiz to go pretty well. The last question on the quiz basically regarded solving for dy after implicitly deriving a function with a given x and a given dx. I found this to be pretty easy and very helpful when I am doing really in depth related rates problems because it is sometimes very hard to remember that you can break up dy and dx into two separate variables.
See the video!