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