# Finding the minimum and maximum distances using Lagrange Multipliers

## Homework Statement

What I don't understand is why you can maximize the distances squared - d2. Isn't d2 different from d? I don't see how they can get you the same value.

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Ray Vickson
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Dearly Missed

## Homework Statement

What I don't understand is why you can maximize the distances squared - d2. Isn't d2 different from d? I don't see how they can get you the same value.
They don't have the same values (unless they happen to be 0 or 1), but they are maximized or minimized at the same points (x,y,z). Think about it: how could it be otherwise?

RGV

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HallsofIvy
Homework Helper
Letting distance be "D", so we can distinguish it from the differential, "d", $d(D^2)/dt= 2D (dD/dt)= 0$. If D itself is not 0, $d(D^2)/dt$ will be 0 if and only if $dD/dt$ is 0.

Ray Vickson