Question

simplify the difference quotient:
f(x+h)-f(x), (h ≠ 0)
as much as possible when
f(x)=5x^2+4x+6

Answer 1

f(x+h) = 5(x+h)^2 + 4(x+h) + 6
= 5(x^2 + 2xh + h^2) + 4 x + 4 h + 6
= 5 x^2 + 10xh + 5h^2 + 4x + 4h + 6
subtract 5 x^2 + 4 x + 6

= 10 xh + 5 h^2 + 4 h

Answer 2

that's what I did too but these are the possible answers:
1) 5x+4+5h
2) 5x-4+5h
3) 10x-4+5h
4) 10x+4
5) 10x+4+5h

that's why I was confused.

Answer 3

They have taken the next step and divided by h

5) 10 x + 5h + 4