Category:Definitions/Second Derivatives

This category contains definitions related to Second Derivatives.
Related results can be found in Category:Second Derivatives.

Let $f$ be a real function which is differentiable on an open interval $I$.

Hence $f'$ is defined on $I$ as the derivative of $f$.

Let $\xi \in I$ be a point in $I$.

Let $f'$ be differentiable at the point $\xi$.

Then the second derivative $\map {f} \xi$ is defined as:

$\ds f := \lim_{x \mathop \to \xi} \dfrac {\map {f'} x - \map {f'} \xi} {x - \xi}$