MHB Which Points Have Specific Characteristics for f', f'', and f'''?

[karush]

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]

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, 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]

I would keep D, as the slope appears to be zero there, and it appears that curvature is changing there also.

 

[karush]

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]

Yes, I think C does not belong, since at that point it appears to me that 0 < f and f'' < 0.