Higher order derivative test
- Higher order derivative test
In mathematics, the higher-order derivative test is used to find maxima, minima, and points of inflexion in an "n"th degree polynomial's curve.
The test
Let be a differentiable function on the interval and let be a point on it such that
#;
# exists and is non-zero.
Then,
#if "n" is even
## is a point of local maximum
## is a point of local minimum
#if "n" is odd is a point of inflection
ee also
* Extremum
* First derivative test
* Second derivative test
* Saddle point
* Inflection point
* Saddle-point method
* Stationary point
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