Question

See attached picture

Answer 1

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

Explanation:

Given

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

Required

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

First, we calculate f(x + h)

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

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

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

So, we have:

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

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

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

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