if f(x) = 2x^2 + 5x,

find f(x+h) - f(x) / h and simplify.

I started to do this but then got lost.
2(x+h)^2 + 5x + 2x^2 + 5x all over h

4x^2 + 4xh + h^2 + 5x + 2x^2 + 5x

2[x^2 + 2 x h + h^2] + 5x + 5 h

2 x^2 +4 xh + 2 h^2 + 5 x + 5 h
-2x^2 -5x

= 4 x h + 2 h^2 + 5 h

divide by h
4 x +2 h + 5

check - limit as h--> 0 should be derivative
4 x^2 + 5 yes check

Well the answer choices were

1) 4x + 5xh + h^2 + 5h
2) 4x + 5h + 4h^2
3) 4x + 5 + 4h^2 + 5h
4) None of the above

So the answer is none of the above correct?

The answer is 4x^2 + 5 correct?

To find f(x+h) - f(x) / h and simplify the expression, we need to substitute f(x) and f(x+h) into the expression and simplify.

Given that f(x) = 2x^2 + 5x, let's find f(x+h) first. To do that, we substitute (x+h) into the function:

f(x+h) = 2(x+h)^2 + 5(x+h)
= 2(x^2 + 2xh + h^2) + 5x + 5h
= 2x^2 + 4xh + 2h^2 + 5x + 5h

Now let's substitute both f(x) and f(x+h) back into the expression f(x+h) - f(x) / h:

[f(x+h) - f(x)] / h = [(2x^2 + 4xh + 2h^2 + 5x + 5h) - (2x^2 + 5x)] / h
= [2x^2 + 4xh + 2h^2 + 5x + 5h - 2x^2 - 5x] / h
= (4xh + 2h^2 + 5h) / h
= (h(4x + 2h + 5)) / h
= 4x + 2h + 5

So, the simplified expression for f(x+h) - f(x) / h is 4x + 2h + 5.