difference quotant

Question

The difference quotient f(x+h)-f(x)/h for f(x)=x²-2x-4

Please help me solve this and explain how to solve. Thanks!

Answer 1

f(x) = x²-2x-4

 

[f(x+h) - f(x)]/h = [(x+h)²-2(x+h)-4 - (x²-2x-4)]/h

 

                       = [x²+2xh+h²-2x-2h-4-x²+2x+4]/h

 

                       = (2xh+h²-2h)/h

 

                       = 2x+h-2