Rate of Change

Question

Find the average rate of change of f(x)=3/x+1 on the interval [x,x+h]. Simplify your answer.

Answer 1

f(x) = 3/(x +1)

 

The exact rate of change is

 

f'(x) = -3 / (x + 1)²

 

The average rate of change over an interval [a,b] is

 

[f(b) - f(a)] / (b - a) = [f(x + h) - f(x)]/[(x + h) - x]

 

= {3/[(x + h) + 1] - 3/(x + 1)}/h

 

You can expand and simplify this if you wish.