SOLUTION: Find the difference quotient f(x+h)-f(x)/h, where h cannot be equal to 0 , for the function below. f(x)=1/x+9 Simplify your answer as much as possible.

Algebra ->  Functions -> SOLUTION: Find the difference quotient f(x+h)-f(x)/h, where h cannot be equal to 0 , for the function below. f(x)=1/x+9 Simplify your answer as much as possible.       Log On


   

Question 1066423: Find the difference quotient f(x+h)-f(x)/h, where h cannot be equal to 0 , for the function below.
f(x)=1/x+9
Simplify your answer as much as possible.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
[f(x+h)-f(x)]/h=
[(1/(x+h+9))-(1/(x+9))]/h=
common denominator is (x+h+9)(x+9)
numerator is x+9-(x+h+9)=-h
so the quotient is -h/h(x+h+9)(x+9), bringing the h in below.
When we use f(x+h)-f(x)/h, and let h approach 0, we have -1/(x+9)^2, which is the derivative of 1/(x+9).