Question

Explain why (see picture) below

Answer 1

if you have you text book, look at the section that says 'derivatives' it should be some where around chapter 4 in you calculus book.
while youre doing that i'll try to answer too!

Answer 2

Unfortunately I don't have textbook, I've been trying to learn calc online. Thanks!

Answer 3

recall the equation for slopes is:
\[m = \frac{ y_2 - y_1 }{ x_2 - x_1}\]

and remember how
f(x) is a fancy way of saying y?

Answer 4

so the slope equation now looks like this:
\[m = \frac{ f(x) - f(x) }{ x_2 - x_1}\]

Answer 5

I understand what a derivative is, what I don't under stand is (see attachment)

Answer 6

now lets make...
\[x_2 - x_1 = h\]

so the slope equation now looks like:
\[m = \frac{ f(x) - f(x) }{ h}\]

we will now have the first f(x), and have x = x+h
so

Answer 7

good to know, i can't ever tell where people are exactly at when they ask questions.
so if you know what a derivative is, then looking at the equation, its saying u'(x) - u'(x) = 0

Answer 8

Sorry for the confusion. But why does the limit of u'(x) as h->0 equal u'(x)?

Answer 9

'the limit of u'(x) as h->0' is a formal way of saying u'(x)

Answer 10

Everything's clear now, really needed that. Thanks!

Answer 11

you're welcome, sorry i didn't get to your actual question sooner!