If you're given a graph of f', how can you tell where there are local min or max in f?

2. Originally Posted by kwivo
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 $f'(x_0 + \Delta x) >0$ and $f'(x_0 - \Delta x)<0$ or the other way around?

maybe, i can't wait for your reply.. anyways, these are the interpretations..
if $f'(x_0) = 0$, then surely, f has a rel min or max at $x_0$
suppose, $f'(x_0 + \Delta x) >0$ and $f'(x_0 - \Delta x) <0$, then f assumes a rel min at $x=x_0$; for the other case, f assumes a relative max.. Ü

3. 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.

4. Originally Posted by kalagota
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 $f'(x_0 + \Delta x) >0$ and $f'(x_0 - \Delta x)<0$ or the other way around?

maybe, i can't wait for your reply.. anyways, these are the interpretations..
if $f'(x_0) = 0$, then surely, f has a rel min or max at $x_0$
suppose, $f'(x_0 + \Delta x) >0$ and $f'(x_0 - \Delta x) <0$, then f assumes a rel min at $x=x_0$; for the other case, f assumes a relative max.. Ü
i think i should have used $\delta x$ there..
maybe this one, if $a < x_0 < b$ such that $f'(x_0)=0$, and $f'(x)<0$ for all $x \in (a,x_0)$ and $f'(x)>0$ for all $x \in (x_0, b)$, then f assumes a rel min at $x=x_0$;
for the other case, i.e. if $f'(x)>0$ for all $x \in (a,x_0)$ and $f'(x)<0$ for all $x \in (x_0, b)$, then f assumes a relative max

5. Originally Posted by kwivo
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.
right..

Originally Posted by kwivo
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.
indeed!!