Real function/Extrema/Higher derivatives/Fact
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Let denote a real interval,
an -times continuously differentiable function, and an inner point of the interval. Suppose that
is fulfilled. Then the following statements hold.
- If is even, then does not have a local extremum in .
- Suppose that is odd. In case the function has an isolated local minimum in .
- Suppose that is odd. In case the function has an isolated local maximum in .