# 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 .