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????

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- Jun 10th 2008, 10:46 AMchris25calc3 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???? - Jun 10th 2008, 11:25 PMCaptainBlack
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