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 f be a differentiable function on the interval I and let c be a point on it such that

1. ;
2. f⁽ⁿ⁾(c) exists and is non-zero.

Then,

1. if n is even
   1. is a point of local maximum
   2. is a point of local minimum
2. if n is odd is a point of inflection.

See also

• Extremum
• First derivative test
• Second derivative test
• Saddle point
• Inflection point
• Saddle-point method
• Stationary point

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