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In my math-book one of the rules of finding maximum and minimum value is:

  • If at x = a, the first and second derivative of a function is $0$ and third derivative is not $0$ then the function at that point does not have a maximum or minimum value.

I can't understand why this is true.

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  • $\begingroup$ Think at $\,y=x^3\,$ around $\,x=0\,$ for example. $\endgroup$ – dxiv Mar 18 '18 at 3:16
  • $\begingroup$ can you provide some details? $\endgroup$ – abu obaida Mar 18 '18 at 9:05
  • $\begingroup$ $y = x^3$ is strictly increasing on $\mathbb{R}$ so it has no extrema. At $x=0$ the first and second derivative ... is 0 and third derivative is not 0 so this is an example of function with the given properties. $\endgroup$ – dxiv Mar 18 '18 at 17:55

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