Question

Given f(x)=3x^2-7x+2, determine f(x+h)-f(x)?

Answer 1

`f(x+h)-f(x)=6xh+3h^2-7h`

Explanation:

`f(x+h)-f(x)=3(x+h)^2-7(x+h)+2-(3x^2-7x+2)`

`f(x+h)-f(x)=3(x^2+2xh+h^2)-7x-7h+2-3x^2+7x-2`

`f(x+h)-f(x)=3x^2+6xh+3h^2+2-3x^2+7x-2`

Simplifying...

`f(x+h)-f(x)=6xh+3h^2-7h`

I will say that you would normally see this question asked:

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

This is the formula associated with finding derivatives in calculus. But if you just need the top (numerator), it is `f(x+h)-f(x)=6xh+3h^2-7h`
Just make sure that you are answering the right question!