essay

Question

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).
(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?