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Happiness
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The following pages use Euler-Lagrange equation to solve for the shortest distance between two points and in the last paragraph mentions: "the straight line has only been proved to be an extremum path".
I believe the solution to the Euler-Lagrange equation gives the total length ##I## a stationary value and not an extremum value, so should the book have said: "the straight line has only been proved to be an extremum path or an inflexion-point path"?
Also, Professor Susskind, I believe, never mentions inflexion-point solutions when he teaches Euler-Lagrange equation, but only extremum and saddle-point solutions.
I believe the solution to the Euler-Lagrange equation gives the total length ##I## a stationary value and not an extremum value, so should the book have said: "the straight line has only been proved to be an extremum path or an inflexion-point path"?
Also, Professor Susskind, I believe, never mentions inflexion-point solutions when he teaches Euler-Lagrange equation, but only extremum and saddle-point solutions.