Car tires need to be inflated properly because over inflation or under-inflation can cause premature tread wear. 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 calculator 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?

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28 42 45 26 35 31 38 66 50 78 70 81 74 59