Higher order derivative test
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In mathematics, the higher-order derivative test is used to find maxima, minima, and points of inflection in an nth degree polynomial's curve.
[edit] The test
Let f be a differentiable function on the interval I and let c be a point on it such that
;- f(n)(c) 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
[edit] See also
- Extremum
- First derivative test
- Second derivative test
- Saddle point
- Inflection point
- Saddle-point method
- Stationary point
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