The Average Rate of Change

Question

Consider the function f(x) = x^2+6 and find the following:

 

The average rate of change of f(x) between the points (x,f(x)) and (x+h, f(x+h)). Assume h>0

 

 

Answer 1

You will use the formula

 

f(x + h) - f(x)

_____________

       h

 

 

 

Then apply f(x) to this difference quotient.

 

(x + h)² + 6 - (x² + 6)

__________________

              h

 

 

Now just simplify.  As you simplify, you should be able to cancel h from the denominator.