(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine the point on a plane curve f(x) = ln x where the curvature is maximum.

2. Relevant equations

k(x) = || T ' (x) || / || r ' (x ) ||

k (x) = f '' (x) / [ 1 + ( f '' (x))^{2}]^{3/2}

3. The attempt at a solution

f ' (x) = 1/x

f " (x) = -1/x^{2}

k(x) = 1/x^{2}/ { [1 + (1/x)^{2}]^{3/2}}

k(x) = 1/x^{2}/ { [ x^{2}+1 /x^{2}]^{3/2}}

iirc we can use the first derivative and try to find the local max...but how do we even start it with this mess? quotient rule? Maybe there's something about the problem that tells us its impossible...? I'm lost here....

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# Finding maximum curvature on lnx

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