- #1

- 13

- 0

^{3}at x=0:

f

^{'}(x)=3x

^{2}f

^{''}(x)=6x ,

for x=0,

f

^{'}(0)=0 & f

^{''}(0)=+ve ,

so it should be a point of local maxima , but it is not!!!!!!!!!!

- Thread starter vikcool812
- Start date

- #1

- 13

- 0

f

for x=0,

f

so it should be a point of local maxima , but it is not!!!!!!!!!!

- #2

- 3,393

- 181

f''(0) is most certainly NOT positive!

- #3

- 9,555

- 766

Since f''(0) = 0 (not +ve, whatever that means), yes, the second derivative test fails. But that doesn't mean you can't determine the type of critical point by other means.^{3}at x=0:

f^{'}(x)=3x^{2}f^{''}(x)=6x ,

for x=0,

f^{'}(0)=0 & f^{''}(0)=+ve ,

so it should be a point of local maxima , but it is not!!!!!!!!!!

- #4

- 258

- 0

^i

It didn't really fail, it just hints at the possibility of an inflection point.

It didn't really fail, it just hints at the possibility of an inflection point.

- #5

- 9,555

- 766

No, it doesn't hint at that any more than it hints at a max or min. You could have max, min, or inflection point when the first two derivatives are zero.^i

It didn't really fail, it just hints at the possibility of an inflection point.

And it does fail as a test distinguishing max/min.

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