Second derivative test for x^3

  • Thread starter vikcool812
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  • #1
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Does the second derivative test fail for x3 at x=0:
f'(x)=3x2 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!!!!!!!!!!
 

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  • #2
jbunniii
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f''(0) is most certainly NOT positive!
 
  • #3
LCKurtz
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Does the second derivative test fail for x3 at x=0:
f'(x)=3x2 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!!!!!!!!!!
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.
 
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It didn't really fail, it just hints at the possibility of an inflection point.
 
  • #5
LCKurtz
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It didn't really fail, it just hints at the possibility of an inflection point.
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.

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

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