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[SOLVED] locate f' f'' and f''' on graph

karush

Well-known member
Jan 31, 2012
2,715
View attachment 442

Which of the points labeled by a letter have

(a) $f'$ and $f''$ non-zero and the same sign B, E

(b) At least two of $f, f', f''$ equal to zero A, C, D

not sure if these selections were correct and was ??? about D in the slope appears to be zero

f' is about slope f'' is about inflection pts and increasing and decreasing I presume

thanks ahead.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
I agree with your answer for a), but I would remove one of the points from b). I don't want to say which, as I want you to re-examine on your own.
 

karush

Well-known member
Jan 31, 2012
2,715
well, i would remove D since has neither zero on x or y axis but my ? is it does have a m=0

not absolute sure what is meant by zero's here
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
I would keep D, as the slope appears to be zero there, and it appears that curvature is changing there also.
 

karush

Well-known member
Jan 31, 2012
2,715
ok how about C since at f it has x=0 at f' it has m=0 but f'' there is no inflection pt.
or is it .....
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Yes, I think C does not belong, since at that point it appears to me that 0 < f and f'' < 0.