Question

See attached picture

Answer 1

`(f(x+h)-f(x))/(h)`
`=2x + h`

Explanation:

Given

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

Required

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

First, we calculate f(x + h)

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

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

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

So, we have:

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

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

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

`(f(x+h)-f(x))/(h)`
`=2x + h`