Question

Hello! I need some assistance with this homework question, pleaseQ7

Answer 1

You have the following function:

`f(x)=x^2+8`

In order to calculate

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

Consider that f(x + h) is given by:

`f(x+h)=(x+h)^2+8=x^2+2xh+h^2`

Then, by replacing f(x) and f(x+h) into the difference quotient and by simplifying, you get:

`\begin{gathered} (f(x+h)-f(x))/(h)=(x^2+2xh+h^2+8-x^2-8)/(h) \\ (f(x+h)-f(x))/(h)=(2xh+h^2)/(h)=(h(2x+h))/(h)=2x+h \end{gathered}`

Hence, the result to the quotient difference is 2x + h