What is the average rate of change of the given function?

Question

Calculate the average rate of change of the given function over the given interval. Where appropriate, specify the units of measurement

f(x)=1/x; [8,9]

Answer 1

To calculate the average rate of change, we need to look at the rate of change (AKA slope) of the function over the end points!

The formula for the slope of a line, f(x), over the interval [a,b] is f(b)-f(a)/(b-a)

So in this case, our function is 1/x and our interval is [8,9]

Therefore, the average rate of change of the function over the interval is

f(9)-f(8)/(9-8) =

(1/9-1/8)/(1)=

1/9-1/8 =-1/72