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Sahithyan's S1
Sahithyan's S1 -- Maths

Higher Order Derivatives

Suppose is a function defined on . is times differentiable or -th differentiable iff:

Here denotes -th derivative of . And means the function itself.

is the -th derivative of at .

Second derivative test

Suppose and is continuous at :

  • a local minimum is at . Converse is not true.
  • a local maximum is at . Converse is not true.

The above conclusion is from Taylor’s theorem when :