Question

Let f (x) = 10/x-4

What is the average rate of change of f (x) from 2 to 8 ?

Enter your response as a decimal.

Answer 1

1.875

Explanation:

The rate of change is the derivative of the function.

`f(x) = (10)/(x-4)\\\\f'(x)=10* \frac {d}{dx}(1)/(x-4)\\\\f'(x)=(-10)/((x-4)^(2))\\\\f'(2) = (-10)/((2-4)^(2)) =-2.5\\\\f'(8)= (-10)/((8-4)^(2)) =-0.625\\`

So, the rate of change is

f'(8) - f'(2) = - 0.625 + 2.5 = 1.875