The function models therelationship between a certain vehicle’s speed and fuel economy, whereis the fuel economy in kilometres per litre and xis the speed ofthe vehicle in kilometres per hour. Determine the rate of change in fueleconomy for 10 km/h intervals in speed, and use your results todetermine the speed that gives the best fuel economy.F(x)F(x)520.005x210.8x112P(t).P(t)P(t)550t211000t120000,CT02_AFSB_C02_064-119.qxd  3/5/09  2:08 PM  Page 78


To determine the rate of change in fuel economy for 10 km/h intervals, we need to analyze the given function that models the relationship between the vehicle's speed and fuel economy. However, the equation you've provided appears a bit disorganized, and I need to clarify the functional form. Based on what is usually given in problems like this, let's assume the fuel economy \( F(x) \) is modeled by the equation:

\[
F(x) = 520 - 0.005x^2 + 10.8x
\]

where \( F(x) \) is the fuel economy in kilometers per liter and \( x \) is the speed of the vehicle in kilometers per hour.

### Step 1: Rate of

The function models the relationship between a certain vehicle’s speed and fuel economy, where F(x) is the fuel economy in kilometres per litre and x is the speed of the vehicle in kilometres per hour. Determine the rate of change in fuel economy for 10 km/h intervals in speed, and use your results to determine the speed that gives the best fuel economy.

This problem explores the relationship between vehicle speed and fuel economy using quadratic functions. Learn how to calculate the rate of change in fuel economy at different speeds and determine the speed that gives the best fuel efficiency. Suitable for high school and early college students, with key concepts from calculus and optimization.

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