Thread: 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????

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 is:



so at a local extremum , so the curvature becomes:



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