Car tires need to be inflated properly because overinflation or underinflation can cause premature treadware. The data in the table show tire life L (in thousands of miles) for a certain type of tire at various pressures P (in lb/in2).
|
P
|
26
|
28
|
31
|
35
|
38
|
42
|
45
|
|
L
|
50
|
66
|
78
|
81
|
74
|
70
|
59
|
a. Use a graphing calculator or computer to model tire life with a quadratic function of the pressure.
b. Use the model to estimate dL/dP when P = 30 and when P = 40. What is the meaning of the derivative? What are the units? What is the significance of the signs of the derivatives?