Question

Simplify the difference quotient

Answer 1

f(x) = 2x+x^2

f(x+h) = 2(x+h)+(x+h)^2

          =2x+2h+x^2+2xh+h^2

[f(x+h)-f(x)]/h =[(2x+2h+x^2+2xh+h^2)-(2x+x^2)]/h

                     =[(2h+2xh+h^2)]/h

                     =h(2+2x+h)/h

                     =2+2x+h