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The function F(x) = −0.005x^2 + 0.8x + 12 models the relationship between a certain vehicle’s speed and the fuel economy, where F(x) is the fuel economy in kilometres per litre and x is the speed of the vehicle in kilometre per hour.
a) Determine the average rate of change in the fuel economy in the interval of speed [60,80].

b) b) Interpret your result.

Respuesta :

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a) The average rate of change on that interval is 0.1

b) as we increase the speed in the interval [60, 80], the fuel economy increases at a rate of 0.1

How to find the average rate of change on the given interval?

For any function f(x), the average rate of change on an interval (a, b) is given by:

(f(b) - f(a))/(b - a)

In this case, the function is:

F(x) = −0.005x^2 + 0.8x + 12

And the interval is [60, 80]

Then we have:

F(60) =  −0.005*60^2 + 0.8*60 + 12 = 42

F(80) = −0.005*80^2 + 0.8*80 + 12 = 44

Then the average rate of change on that interval is:

R = (44 - 42)/(80 - 60) = 0.1

b) What does that rate means?

F(x) relates the fuel economy and x the speed of the vehicle.

This means that as we increase the speed in the interval [60, 80], the fuel economy increases at a rate of 0.1.

If you want to learn more about average rates of change:

https://brainly.com/question/8728504

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