INTRO: Many students are faced with those stressful weeks of studying over the course of the semester. From exams to tests and homework the life of a college student can get pretty stressful. All of these factors contributed to our group trying to minimize the stress level of a college student through study habits. Our input variable was how many hours the student (Emmett) studied each day. Our output variable was the amount of stress felt measured on a subjective scale. The scale ranged from 0-100 with 0 meaning the student felt no stress and 100 meaning he felt extremely stressed. The data will be controlled through the use of one student recording his stress levels. The results are randomized naturally because the student will be studying based on the amount of work he has each night. Our guesstimate is the less the student studies, the less his stress will be, meaning the closest number to zero will probably be the minimizing point.

DATA:

Hours Studying (t)
Stress Level
2.5
80
1.5
30
1
50
3
90
2.5
60
0.5
0
1
20
2
70
2
80
3.5
100
2
30
1.5
20
0.5
10
2.5
80
1
0

Model 1:
The first model that we created was a cubic model. The equation we got for the model is shown on the graph. The derivative of this model is y’=-11.499132x2+44.282286x-2.894639. To find critical points of this derivative, we needed to set the derivative equal to zero. When we do that, using the quadratic formula, we find that there are critical points at (3.784407, 91.5647642) and (.066516818, 3.072159026). It is important to note that the x value of 0.066516818 is not shown on the trend line, however if the line were continued to the y-axis, the point would be seen. After identifying the critical points, it is necessary to find the second derivative of the function and use the second derivative test to determine whether our critical points are