1. ## calc3 concept

given a twice differentiable function y = f(x), determine its curvature at a relative extremum. Can the curvature ever be greater than it is at a relative extremum? why or why not....

i cannot picture this????

2. Originally Posted by chris25
given a twice differentiable function y = f(x), determine its curvature at a relative extremum. Can the curvature ever be greater than it is at a relative extremum? why or why not....

i cannot picture this????
The curvature of a plain curve given by an explicit equation $y=f(x)$ is:

$\kappa=\frac{|y''|}{(1+y'^2)^{3/2}}$

so at a local extremum $y'(x)=0$, so the curvature becomes:

$\kappa=|y''|$

at such a point.

The curvature can be smaller than that at a local extrema, but I will leave it to you to work out why.

RonL