Question

Determine (a+h) - @) for f(x) = x2 + 5x and simplify.

Answer 1

`f(a+h)-f(a)=2ah+h^2+5h`

Explanation:

Given function is
`f\left(x\right)=x^2+5x`.

Using that function, we need to determine the value of f(a+h)-f(a).

`f\left(x\right)=x^2+5x`

`f\left(a+h\right)=(a+h)^2+5(a+h)`

`f\left(a+h\right)=a^2+2ah+h^2+5a+5h`

similarly

`f\left(a\right)=a^2+5a/tex]</p><p>Then [tex]f(a+h)-f(a)=(a^2+2ah+h^2+5a+5h)-(a^2+5a)`

`f(a+h)-f(a)=a^2+2ah+h^2+5a+5h-a^2-5a`

`f(a+h)-f(a)=2ah+h^2+5h`

Hence final answer is
`f(a+h)-f(a)=2ah+h^2+5h`.