If you're given a graph of f', how can you tell where there are local min or max in f?
what does it mean when f'(x)=0?
what are the intervals where f'(x)>o and f'(x)<0?
what does it imply when $\displaystyle f'(x_0 + \Delta x) >0 $ and $\displaystyle f'(x_0 - \Delta x)<0$ or the other way around?
maybe, i can't wait for your reply.. anyways, these are the interpretations..
if $\displaystyle f'(x_0) = 0$, then surely, f has a rel min or max at $\displaystyle x_0$
suppose, $\displaystyle f'(x_0 + \Delta x) >0 $ and $\displaystyle f'(x_0 - \Delta x) <0$, then f assumes a rel min at $\displaystyle x=x_0$; for the other case, f assumes a relative max.. Ü
When f'(x)=0, that's a critical point. If f'(x)>0, then that's where f(x) is increasing; f'(x)<0, f(x) is decreasing.
I don't get what the last one mean.
Ok, so I got local max at x=2. Then I got min at x=4,x=8. Am I missing something for max because I didn't get the right answer.
i think i should have used $\displaystyle \delta x$ there..
maybe this one, if $\displaystyle a < x_0 < b$ such that $\displaystyle f'(x_0)=0$, and $\displaystyle f'(x)<0$ for all $\displaystyle x \in (a,x_0)$ and $\displaystyle f'(x)>0$ for all $\displaystyle x \in (x_0, b)$, then f assumes a rel min at $\displaystyle x=x_0$;
for the other case, i.e. if$\displaystyle f'(x)>0$ for all $\displaystyle x \in (a,x_0)$ and $\displaystyle f'(x)<0$ for all $\displaystyle x \in (x_0, b)$, then f assumes a relative max