Thread: question about graph

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

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 and or the other way around?

maybe, i can't wait for your reply.. anyways, these are the interpretations..
if , then surely, f has a rel min or max at
suppose, and , then f assumes a rel min at ; 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.

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 and or the other way around?

maybe, i can't wait for your reply.. anyways, these are the interpretations..
if , then surely, f has a rel min or max at
suppose, and , then f assumes a rel min at ; for the other case, f assumes a relative max.. Ü

i think i should have used there..
maybe this one, if such that , and for all and for all , then f assumes a rel min at ;
for the other case, i.e. if for all and for all , then f assumes a relative max

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!!