- #1
lLovePhysics
- 169
- 0
I've been thinking... Since derivatives can be written as:
[tex]f'(c)= \lim_{x\rightarrow{c}}\frac{f(x)-f(c)}{x-c}[/tex]
and for the limit to exist, it's one sided limits must exist also right?
So if the one sided limits exist, and thus the limit as x approaches c (therefore the derivative at c) (but f(x) is not continuous at c) why can't f(x) have a derivative at c?
I'm just looking at it from that standpoint (I know that derivatives are basically the rate of change of a function at a point or in general).
[tex]f'(c)= \lim_{x\rightarrow{c}}\frac{f(x)-f(c)}{x-c}[/tex]
and for the limit to exist, it's one sided limits must exist also right?
So if the one sided limits exist, and thus the limit as x approaches c (therefore the derivative at c) (but f(x) is not continuous at c) why can't f(x) have a derivative at c?
I'm just looking at it from that standpoint (I know that derivatives are basically the rate of change of a function at a point or in general).