Thread: Learning Derivatives

Beginner. Working on this problem: Use the definition of a derivative function to calculate f'(4) where f(x) = x + 3.
Have made attempt using lim h->0 [f(x+h) - f(x)]/h but unsure if answer is correct. Need explanation. Help!

Originally Posted by Yami Sorceress

Beginner. Working on this problem: Use the definition of a derivative function to calculate f'(4) where f(x) = x + 3.
Have made attempt using lim h->0 [f(x+h) - f(x)]/h but unsure if answer is correct. Need explanation. Help!

Now simplify and take the limit? Got it?

Hint: the limit is constant

There is an equivalent definition that is sometimes useful:



so

OK, so for clarity I could write:

lim h->0 (x+3)+h - (x+3) / h

simplify:
lim h->0 h/h = 1 ?

Where does the f ' (4) fit in?

Originally Posted by Yami Sorceress

OK, so for clarity I could write:

lim h->0 (x+3)+h - (x+3) / h

simplify:
lim h->0 h/h = 1 ?

Where does the f ' (4) fit in?

Thank you for the clear example.

Originally Posted by Yami Sorceress

Where does the f ' (4) fit in?

What you must understand is that for ALL x. So, , . All x. This makes sense right? because the slope of a line is constant right?