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 $\displaystyle y=f(x)$ is:
$\displaystyle \kappa=\frac{|y''|}{(1+y'^2)^{3/2}}$
so at a local extremum $\displaystyle y'(x)=0$, so the curvature becomes:
$\displaystyle \kappa=|y''|$
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