Question

Find and simplify the difference quotient for the given function

Answer 1

`(f(x+h)+f(x))/(h)`

Replace f(x) and f(x+h) by using the equation given for the problem.


`=((2(x+h)^2-(x+h)-1)-(2x^2-x-1))/(h)`

Open all parenthesis


`= (2x^2+4xh+2h^2-x-h-1-2x^2+x+1)/(h)`

Factor the h


`= (h(4x+2h-1)+2x^2-2x^2+1-1+x-x)/(h)`

Other terms not in the parenthesis cancel each other out


`(h(4x+2h-1))/(h)`

Now, simplify


`=4x+2h-1`