Question

So I have g (x) = x squared + 2x

Then I have g (a + h) - g (a) all over h, and I'm supposed to solve this

I ended up with 2ah + 4a + 2h + 2a squared all over h, but the answer should be 2a + 2 + h.

What did I do wrong?

Answer 1

i believe this problem is finding the derivative of a function using the limit as h approaches 0. the answer should simply 2a + 2

Answer 2

Well, that's not what my textbook says

Answer 3

I just want to know how to get to the final answer, because at this point, I am completely stumped

Answer 4

it would be:
limit as h approaches 0 of:
[ (a+h)^2 +2(a+h) - a^2 - 2a ] / h
=
limit as h approaches 0 of:
[ a^2 +2ah + h^2 +2a + 2h - a^2 - 2a ] / h
=
limit as h approaches 0 of:
[ 2ah + h^2 + 2h ] / h
=
limit as h approaches 0 of:
2a + h + 2
= 2a + 2

Answer 5

my bad, just realized you aren't using limits. meaning it stops at the before last line, which is what your textbook says :)

Answer 6

You are my hero right now...thank you for working this problem