54. Car tires need to be inflated properly because overinflation or underinflation can cause

54. Car tires need to be inflated properly because overinflation or underinflation 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/in^2).

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

(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?

Calculus: Early Transcendentals
Chapter 3: Differentiation Rules
Section 3.1: Derivatives of Polynomials and Exponential Functions
Problem 54

Video 1174 of Hourly Uploads - 10/19/2023 - 792 Subscribers - 151,180 Views