I've gotten an answer for the first half of this, but not the second one, which I believe is some sort of trick question.

Find the maximum and minimum values of

on the curve

by the method of Lagrange Multipliers.

I already have this half answered, and got the following:

Max:

Min:

,

Now for the second half, which I believe is some sort of trick question.

If

is substituted into

, we get a function

, which has only a maximum value on

. Explain how the extreme values obtained in the first part can be obtained from

.

See, the issue is that

is a parabola, which has a maximum at 5, but no minimum (or at least no absolute minimum). So how would you use

to find the minimum values? That's what I feel is the "trick" part of the question.

If anyone could clarify the second half of the question, I'd appreciate it.