Question

1Compute the difference quotientf(x + h) - f(x)hfor the function f(x) =Simplify your answer as much as possible.X + 2f(x +h)-f(x)h

Answer 1

We will compute this as:

`\begin{gathered} (f(x+h)-f(x))/(h)=(1)/(h)(f(x+h)-f(x))=(1)/(h)((1)/((x+h)+2)-(1)/(x+2)) \\ (1)/(h)(((x+2))/((x+h+2)(x+2))-((x+h+2))/((x+h+2)(x+2))) \\ \\ (1)/(h)((x+2-x-h-2)/((x+h+2)(x+2))) \\ \\ (1)/(h)((-h)/((x+h+2)(x+2)))=(h)/(h)((-1)/((x+h+2)(x+2)))=(-1)/((x+h+2)(x+2)) \\ \\ (-1)/(x^2+2x+hx+2h+2x+4)=(-1)/(x^2+(4+h)x+(4+2h)) \end{gathered}`