1.So far all my group members are on point. We already did both our Fed Ex Express (130 inches) and UPS (165 inches) graphs, as well as our tables. We have generalized and checked our volumes, girth, length, width and height using calculators.

The design I used for FedEx Express was the width and the height are the same. This would make the box a square face, which means the formula i used to find the girth was x+x+x+x or 4x. Since i knew that X, the width and the height would be the same all i had to do was find my length. The way i found my length was by subtracting the total by the girth, in this case it would be (130-4x). Now i had to find the volume. The way i found the volume was by multiplying the length, width,and height. I generalization for the volume was (130-4x)x*x.

The design i used for UPS was the width is always 10 inches longer than the height. This design would make the box a rectangular face, which means that the formula i used to find the girth was w+h+w+h or 4x. In this problem my width and height werent the same anymore, but my height and x would always be the same. So in order to find the width i had to add 10 to the height becuase my design said that the width is always 10 inches longer than the height(x+10). now i had to find my length so i did the same thing i did with the FedEx Express box, i subtracted the total from the girth (165-4x). the next thing i had to was find the volume. I found the volume by multiplying the width, length , and height. My generalization for the volume was (x+10)(x)(165-4x) .

My group memebers and i checked all our calculations inoreder to see what our scale on the graph would be. It was very hard at first becuase we werent sure how to scale it, but then it worked out. When we were done i checked my tables first to do the finite differences so that i can see whether my calculations were correct, and to see if when i graphed my points it would be a 3rd degree polynomial. Then i felt i was ready to start graphing. For my FedEx Express graph my y- axis scale was 3,000's and my x -axis scale was 1's. My y-axis was labeled volume and my x-axis was labeled just plane ol (x). As my graph was completed i plugged in my function in the calculator, put in my scale and pressed graph to see whether my graph matched the one on the calculator and it did. Then i pressed 2nd graph on the calculator to see if my maximum point was correct and it was. I didnt use the trace thing on the calculator to find the maximum volume becuase i find that to be very confusing, instead i looked at my table and my graph.

My maximum volume for FedEx Express was 20,328 (22,20328) and for UPS it was 40,227 (23,40227).

The way i organzied was by creating a table. My first two tables had the total, (x), length, width, height, volume , and girth. It also had all my functions for each column. Then i made two T -charts with only x and the volume. I used this chart to check the finite difference. Unfortunately everyone in my group had to create their own tables becuase we all had different designs and the shipping was different as well.

3. When my group members and i were done with all our calculations and graphing we looked at our maximum volume for FedEx Express and UPS. Michelle's and my maximum volume for FedEx Express was 20,328. Tyre's maximum volume was 20,342 and it was the highest. I think his was different because he had a different design from the both of us. Like his design was for FedEx Express was the width is always 6 inches longer than height and mines was the width and the height are the same. For UPS we all had different maximum volumes. My maximum volume was the highest. The reason for this was because we all had different designs for our boxes too. Like my UPS design was the width is always 10 inches longer than the height. Meaning like if my height was 1 then my width would be 11 because i added 10 to 1 (x+10). Since my design was the width is always 10 inches longer than the height, that means the width is longer than the rest of my group members and its more flat.