Math Curve sketching Curvature behavior

Curvature behavior

Curvature is the change in direction of a function graph at a point (inflection point).



As a reminder, you can ask in which direction you would have to steer, if you leave the function graph from left to right.
The direction then decides if the function is left or right curved.
Curvature behavior


The curvature behavior in one interval can be determined with the second derivative.

The function is twice differentiable on the interval $I$ and

  • left-curved if $x\in I$ for all $f''(x)>0$
  • right-curved if $x\in I$ for all $f''(x)<0$