Before you learn how to do derivaties in the normal way, you calculate them using limits. The general formula looks like this:
If you try this for, for instance, f(x) = x^2, you'll see you can pretty easily get to f'(x) = 2x. (The general trick, if this all looks completely unfamiliar, is to somehow massage the formula until it's solvable with h = 0.)The one I couldn't solve was the one where f(x) = sqrt(1 + 2x). The formula for the limit looks like this:
I'm pretty sure I'll have to multiply by some kind of square root to get the thing solved, but so far no luck. (As a reminder, I do know the actual answer - this is an odd-numbered question, after all - so what I'm looking for is how to actually calculate this limit.)
Your answer is nearly right but not quite - I suspect a simple math error somewhere.
ReplyDeleteBut now the question is, can you (or someone else) explain how to get there (hopefully without 11 pages of work!)
Multiply both denominator and numerator by [sqrt(1 + 2(x+h) ) + sqrt(1+2x) ]
ReplyDelete