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Hey, let's see if I can remember how to do it, the answer that was previously mentioned (#1) is correct, and it can easily be solved by the chain rule[which is second nature, once you learn it]. However, what you are given here is the formal definition of a limit. To see how to get the answer of 6x+4 here are the complete mathematical steps:
Ok the first part says f(x+h), so that means take your f(x) equation and h to every x term you see:
3(x+h)^2 + 4(x+h) + 2
and that's basically it, now apply the equation
lim as h->0 f(x+h) - f(x) / h
so... we have:
lim h->0 (3(x+h)^2 + 4(x+h) + 2 - [3x^2 + 4x + 2]) / h
lim h->0 (3x^2 + 6xh + 3h^2 + 4x + 4h + 2 - [3x^2 + 4x + 2]) / h
now, perform some cancellations and you have:
lim h->0 (6xh + 3h^2 + 4h) / h now.. you see a common factor of h, which can also be cancelled, so you're left with:
lim h->0 (6x+3h+4)
ok, you may be saying what!?! that's not the answer.. now, you simply plug in 0 for h, so you have as a final answer: f`=dy/dx = 6x + 4
Hope this clarifies your problem and closes the book on this thread :-)
P.S. Make sure you continuously write lim h->0 for each step as I did, teachers are notorious for taking points off for not including that, since it is a formal definition of a limit.
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