# Rules of finding maxima and minima of a function

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.

• Think at $\,y=x^3\,$ around $\,x=0\,$ for example. – dxiv Mar 18 '18 at 3:16
• can you provide some details? – abu obaida Mar 18 '18 at 9:05
• $y = x^3$ 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. – dxiv Mar 18 '18 at 17:55