Difference Quotient problem with understanding completely: f(x)=1/x^2

Question

f(x)=1/x^2 In utilizing the difference quotient to solve this problem, how would I solve it? Please list in steps as well. 

Thank you in advance.

Answer 1

Difference quotient is defined as

 

 

lim             f(x + h) - f(x)

h-->0      ______________

                        h

 

 

lim           [1 / (x + h)²] - [1 / x²]

h-->0      _____________________

                          h

 

 

Now simplify the difference quotient.  Also, due to the fact that zero cannot be in the denominator, you will need to do some factoring and cancelling so the h in the denominator goes away.